The Uruguay international joins on a one-year contract with the option to extend for a further year.
Cavani, who has won the Golden Boot in both Ligue 1 and Serie A, has scored 341 goals at club level since moving to Europe in 2007, including 35 in the UEFA Champions League. The forward won six league titles with Paris Saint-Germain and, with 200 goals, is their all-time leading scorer. Internationally, Cavani won the Copa America in 2011 and has found the net 50 times in 116 appearances for Uruguay.
Edinson Cavani said: “Manchester United is one of the greatest clubs in the world, so it is a real honour to be here.