The striker who is a free agent after leaving his former club PSG signed a one year contract with United with an option to extend for a further year.
A statement from the club reads: "Manchester United is delighted to announce the signing of striker Edinson Cavani."
Cavani has scored 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.