Friedrich Witt was born on 8 November 1770 in Niederstetten. At about 17 he came to the court of Oettingen-Wallerstein to complete his musical training. He was probably a pupil of Antonio Rosetti (1750–1792). The Wallerstein archive holds an appointment decree for Friedrich Witt dated 21 January 1790, stating that Witt, from Mergentheim (!), had been employed by the court orchestra since 1 October with an annual salary of 300 guilders. In this orchestra he served as cellist.
The prince repeatedly granted Witt leave for concert tours. He undertook several of these together with the clarinetist Joseph Beer (1770–1819), who was likewise engaged at Wallerstein, travelling for instance to Potsdam, Ludwigslust and Vienna. Witt probably spent an extended period in Vienna from 1796 onward. In 1802 he was appointed court Kapellmeister by the Bishop of Würzburg, a post he held until the court music establishment was dissolved in 1814. From 1804 he was additionally music director at the newly founded Würzburg municipal theatre. Highly honoured, he died on 3 January 1836 in Würzburg.