Anna Selina Storace, known as Nancy to her closest friends, was born in London on 27 October, 1765 to Stefano (1725-1781) and Elizabeth Storace (née Trusler). Stefano Storace moved to Dublin from his native Italy at the age of 23, relocating 10 years later to London while working as a double-bass player. In 1761 he married Elizabeth Trusler, who was the daughter of the proprietor of Marylebone Gardens. Their first child, Stephen (1762-1796), who would later become a popular composer of comic operettas, is known at the Father of the Musical.

Anna began studying voice in London with the castrato, Venanzio Rauzzini, for whom the young Wolfgang Amadeus Mozart composed his Exsultate jubilate in 1773. By the time she was eight years of age, Anna was singing before royalty and performing throughout England. In 1778, at the age of 13, she went to Naples, accompanied by her parents, to visit Stephen, who had been studying composition at the Conservatorio San Onofrio for three years. Her debut Italian performance was at the Teatro allo Pergola in Florence in 1780, where it was reported she enjoyed such success that the castrato Luigi Marchesi, who performed alongside her, demanded she be dismissed from the troupe. Further performances took place at Lucca, Livorno, Parma, Milan, and Venice. It was in Venice that Anna, Irish tenor Michael Kelly, and Italian baritone Francesco Benucci were approached by Count Durazzo, who had been sent by Emperor Joseph II of Vienna to hire singers for his new project, the Imperial Italian Opera Company. In the meantime, Anna's father returned to London only to fall ill and die just at the onset of his daughter's success. The singers, accompanied by Elizabeth, traveled together to Vienna, where they remained for four years.

Anna made her Viennese debut on 22 April, 1783, as the Contessa in Antonio Salieri's La Scuola de'Gelosi, and went on to perform in numerous other operas. Anna's star rose quickly in Vienna and she soon found herself the toast of the city, celebrated as the favored prima buffa at the Burgtheater. She had a strong voice of an amazing range, solid technique, and her acting was lively and delightful. Impresarios and composers adored her for her indefatigable spirit and her willingness to lend a hand wherever one was needed. In 1784 Anna married John Abraham Fisher, an older English composer and violinist who was on an enforced sabbatical from Oxford. The marriage was apparently her mother's doing and was against the advice of Anna's friends. Fisher beat Anna mercilessly, which caused the actress try to hide her bruises with make-up when appearing on stage. When word of the beatings got out, Emperor Joseph II, concerned about his prize singer and actress, banished Fisher from Vienna. Not long after this, Anna announced that she was pregnant, but she continued to work until, at the premier of her brother's opera in 1785, Gli Sposi Malcontenti, she collapsed onstage and was unable to speak for four months. During this time, she gave birth to a daughter, who was given to a foundling home and died not long after. After her recovery, Anna returned to the stage on September 26. Her popularity with the Viennese was so great that a cantata, Per la Ricuperata Salute di Ophelia was jointly composed in her honor by Mozart, Salieri, and Cornetti, with the text written by Lorenzo Da Ponte. Ophelia was the role Anna was currently preparing for Salieri's latest opera, La Grotta di Trofonio, so the title of this cantata was in reference to that character. Anna made final Burtheater performance on 19 February, 1787, in Martín y Soler's Il Burbero di Buon Cuore. This was followed by a farewell concert at the Körntnertor Theater on 23 February, at which Anna performed Ch'io mi Scordi di te?...Non Temer, Amato Bene, K.505, a grand concert aria Mozart had composed for her, accompanying her on his fortepiano.

During her years in Vienna, Anna's name had been linked romantically with several men besides John Fisher, including composer Vincente Martín y Soler, Francesco Benucci, who sang the title role in Le Nozze di Figaro, Lord Barnard (William Henry Vane of London, who later became the Earl of Darlington in 1792 and the 1st Duke of Cleveland in 1833), Mozart, and even Emperor Joseph II. However, when one studies her grueling rehearsal and performance schedule it is easy to see that these would have been short-lived affairs, if they indeed existed at all; the only two that have been sufficiently documented are Fisher and Benucci. Indeed, Anna maintained an amiable friendship with Benucci after their breakup following the run of Figaro and in 1789, the two paired up once again to perform in concert at The King's Theatre in London, where they performed selections from Figaro and Don Giovanni, as well as some duets by Salieri. When Anna left Vienna at the end of February of 1787, she was accompanied by her mother and brother, and Michael Kelly, who had sang the roles of Don Curzio and Don Basilio in Figaro, Mozart's pupil Thomas Attwood, and Lord Barnard. There were plans in the offing for Anna to return to Vienna in 1788, but these fell through because the Emperor could not pay her what she required, due to Austria's war with Turkey.

Anna opened in London, in Paisiello's Gli Schiavi per Amore on 25 April, 1787, in which she had also appeared in Vienna under the original title of La Gare Generose. In this, she appeared as an African slave. This production was more successful than the Viennese production, for London audiences had not been given true comic opera for a number of years. Anna's acting was refreshing and authentic, and she immediately won their hearts. In the audience was the Prince of Wales, George IV, who also attended the following night's production. It was observed that he arrived before the beginning of the overture, which was apparently out of character for him. He came again on the 28th. No doubt Anna's comedic flair pleased the prince, as "The enchanting Storace was beating time with her garden clippers", as was reported in the Morning Chronicle. Through this friendship Anna was able to secure for Mozart an invitation to come to London to produce Figaro. By the time this came through, however, Mozart was too ill to accept.

In July, London held its annual Handel Commemoration Festival at Westminster Abbey and Anna was invited to sing the most popular soprano piece in Messiah, that is, I Know That My Redeemer Liveth, as well as Let the Bright Seraphim from Samson.

Despite the Storace family's hopes that they would not hear from Fisher after taking their leave from the continent, he made his presence known within the year. Perceiving that Anna's popularity could only grow, possibly making her a wealthy woman, Fisher secured lawyers to make her an offer: he would never appear in the same country as she as long as she paid him an annual stipend of £10. Seeing this for the blackmail it was, Anna refused to meet his terms. For some reason Fisher abandoned his suit. He later toured Europe and settled down in Ireland, where he was employed as a music teacher. He died there in 1806.

Anna and her brother became nearly inseparable and joined together at Drury Lane to turn out a dizzying number of operas until Stephen's death in 1796. They spent nearly every minute of their lives together either in rehearsals or performances, with he as composer and conductor and she as the prima buffa. Although Stephen married and had a son, he spent more time at his sister's house than at his own. Stephen seems to have offered her more than a husband could, with mutual interests and goals, and marriage was something Anna was to forever after avoid. Stephen's style of musical comedy fitted Anna like a glove and the public adored her performances in which she was consistently cast as the soubrette, opposite the leading man. Each role seemed to be a variation of the role of Susanna in Figaro: the clever young maid who could outwit any lecher who set out to conquer her. Because these roles were often ethnic, Anna's dark complexion and curvy figure were perfect. These roles did not demand a stately, serene beauty, and Anna could look every bit the part of a slave, servant girl, or gypsy.

Between the months of November 1791 and May 1792, Anna was gravely ill with what appears to have been a brain hemorrhage, and she nearly died the exact night that Mozart died in Vienna, 5 December, 1791. A trepan procedure was performed to ease pressure on the brain, however, and she recovered, although she was weak for many months. As soon as she was able, Anna returned to the stage with all the energy and zeal she'd had in the past. In the summer, she was contracted to sing Handel's Messiah at the King's birthday celebrations. During the performance, however, as she sang the final cadence of I Know That My Redeemer Liveth, a Quaker woman stood and shouted, "O fie on thee! Shame! Shame! It is rank idolatry!". The woman was quickly escorted out of the cathedral. In those times, women singing solos in a church was not looked on with favor, much less women of the theatre who were considered to be only one step above the rank of a prostitute.

The newly rebuilt Drury Lane re-opened in March of 1794 and by the end of 1795, Stephan had fallen seriously ill, but continued to turn out his operas. It is assumed that he had a brain tumor. He died on 16 March, 1796, at the age of 33. Anna was understandably prostrate with grief, although she returned to work after only six weeks, a fact that did not escape her most hardened critics.

In 1797, Anna began to take a more active role in society and was seen with John Braham, a new, talented tenor who had premiered in Stephen's Mahmoud, in 1796. Braham, who was 11 years Anna's junior and trying to establish himself in the London theatre, had everything to gain from this relationship and the two embarked upon a tour of Europe in August 1797. However, upon arriving at Calais, they were immediately detained by the police for not having passports. These were troubled times in Europe, especially France, and travelers from England carrying no passports were quickly assumed by Napolean's police to be spies. Nevertheless, they were requested to perform for Napoleon and Josephine twice in October. The tour took them to Florence, Milan, Naples, and Venice.

In Naples they met Admiral Nelson and his mistress, Emma Hamilton, with whom Nancy formed a close, lifelong friendship. After performing in Venice, Anna and Braham traveled north to Vienna, where she was hardly remembered since both Emperor Joseph II and Mozart were dead. This must have been a difficult time for her. When they returned to London in September 1801, Anna was pregnant. Her son, William Spencer Harris Braham, was born on May 3, 1802.

The following Autumn, Anna and Braham returned to Drury Lane, which was managed by Michael Kelly, performing in The Siege of Belgrade on 2 November. News of Admiral Nelson's death quickly consumed Lo ndon, however. When the Admiral's body was returned to London, Braham was asked to sing at the funeral service, with Anna sitting next to Lady Hamilton, who had been, not unsurprisingly, omitted from the Nelson Family's guest list.

Anna finally decided to retire from the stage after the 1807-1808 season was completed. Her final performance was on May 30, 1808 in her brother's opera, No Song, No Supper. In January of 1809, Anna moved herself, Braham, and six year-old Spencer into Herne Hill Cottage, a country house in Lambeth, that was designed and built by the English architect, John Soane. After 18 years together, Braham and Anna parted ways in 1814. Embarrassing and scandalous lawsuits ensued, with Braham trying to lay hands on the material possessions Anna had bought with her own money. Throughout his life, Spencer maintained that it was the break with Braham that caused the decline of his mother's health, as well as her death. Anna retained her property, but suffered a stroke in the summer of 1817, and a couple of days later had a second stroke, dying at 1:30 pm on 24 August, with her old friend Michael Kelly at her bedside. Her funeral was on 2 September and was attended by her many friends and her small family. She was buried in the churchyard of St. Mary's Lambeth, where her mother, Elizabeth donated a plaque to be inserted into the wall.