The theme was borrowed from the second movement of Trio Sonata No. 8 from Albinoni's Trio Sonatas, Op. 1 (Venice, 1694). Among the three so-called "Albinoni Fugues" (BWV946, 950, 951), this is the largest and most substantial fugue. It is also one of Bach's earliest works in B minor. In later years, Bach composed solemn works in B minor, including the Mass, and the genesis of these can be seen here.

A thoroughly revised later version, BWV 951a, exists for this piece. Crude counterpoint and forbidden progressions were corrected, and old cadential formulas and clichés were eliminated. The tonal structure was re-examined, new sections were added, and a clearer recapitulation was provided, transforming the improvisatory flow of the early version into a symmetrical work. While the overall atmosphere and structure remain unchanged, the archaic qualities and redundancies often found in early works were removed, resulting in a fully mature style.

It appears that Bach continued to revise the work even after the major overhaul, right up to his Leipzig period, as various manuscript copies with differing details remain. Furthermore, BWV 951 and 951a often appear as a pair in later manuscript sources, suggesting that many musicians studied them as a prime example of Bach's revision process. The pairing with the early work Fantasia in B minor, BWV 923, is not thought to be Bach's own idea, but it is transmitted in several sources, indicating that this work was widely disseminated and practiced.