The Uruguayan striker joined the Premier League club on transfer deadline day, along with Brazilian left-back Alex Telles.
The Red Devils turned their attention towards the 33-year-old after failing to land number one target Jadon Sancho from Borussia Dortmund.
Cavani left Paris Saint-Germain at the end of his contract in June after seven successful seasons in Paris where he became the club's all-time record goal-scorer with 200 in all competitions.
"Manchester United is delighted to announce the signing of striker Edinson Cavani.
"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.