The Montenegro international has departed after three years in Turin, with Al Jazira paying €6.3million for his services.
Vucinic moved to Juve in August 2011, and has helped the club to the Scudetto in each of his three seasons at Juventus Stadium.
A regular in his first two campaigns in Turin, Vucinic fell out of the first-team picture under Antonio Conte last term as he battled knee injuries.
Juve attempted to use him as a makeweight in a January move for Inter midfielder Fredy Guarin, though the deal collapsed after the Milan club's fans revolted against the potential transfer.
He will now continue his career in the Emirati top flight, in which Al Jazira placed third in last term - earning qualification to the AFC Champions League.
Burkina Faso winger Pitroipa joins the club after three seasons with Rennes, scoring 19 goals in 112 games for the Breton club.
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