Mozart undertook his third and final Italian visit between October 1772 and March 1773. The 17 year old youth – accompanied by his father – travelled to Milan where he had been commissioned to write a new opera: Lucio Silla  which was premiered on December 26th. In the following month, Mozart composed his solo motet Exsultate, jubilate for the primo uomo, male lead of the opera, Venanzio Rauzzini. Rauzzini was from Rome and one of the best known castrato sopranos of the era; the English traveller Burney reported that he was not only a superb singer with a striking appearance and a fine actor, but also a master of counterpoint and a superb Klavier player. Rauzzini also composed, writing operas, string quartets and sonatas. His abilities as a singer can be well sensed from Mozart's work: not only could he relax his listeners with his melodic qualities but the fast movements with their great interval leaps suggests he must have given a bravura performance at its premiere on January 17th, 1773.

The structure of the three movement Exsultate, jubilate has been explained by a number of people. Hermann Abert described it as a dramatic solo cantata, while twentieth century musicologists have been more inclined find similarities with the symphonies Mozart composed as this time. The great Bach and Mozart researcher, Alfred Einstein pointed out the similarities with the so-called “Italian overture” type: the Exsultate, jubilate fast – slow – fast structure adheres to this perfectly. It differs from this scheme in two ways: the second section is preceded by a brief recitativo while the finale is connected to the second movement through a simple modulation with no break. Mozart's solo motet, despite its religious text, is musically not in “church style”, indeed it derives much from the operas of the era. This is more apparent in the second movement, which Einstein, with justification, called the cavatina. The work is permeated throughout, in the words of Einstein, by the good spirits and dynamism of youth. This is naturally not in conflict with the text which is about joy and jubilation. The F major opening movement is a kind of vocal concerto which emulates the accepted structures of Viennese classical concertos. The orchestra has a concise exposition consisting of only twenty one bars, which introduces the movement's thematic material in the basic tonality, after which comes the much longer solo exposition which – as appropriate for sonata form – concludes in the dominant. However, the development section is omitted, instead Mozart launches the recapitulation in C major (in other words, the “wrong key”). Before the movement is closed – just as in an instrumental concerto – the soloist is given the opportunity to improvise a cadenza. After a graceful, intimate second movement, the finale is given over to cloudless joy. It is interesting, although probably a coincidence that at the end of the work, the theme strongly suggested Haydn's famous imperial hymn, Gott, erhalte, today the German national anthem.