It was confirmed on Saturday that the 33-year-old had held discussions with the club and he secured his move to Old Trafford ahead of Monday’s 11pm transfer deadline.
Cavani left Paris Saint-Germain at the end of last season after scoring 187 goals during his seven years in the French capital.
“Manchester United is one of the greatest clubs in the world, so it is a real honour to be here,” said the Uruguay international.
“I’ve worked really hard during the time off and I feel eager to compete and represent this incredible club.
“I have played in front of some of the most passionate supporters in football during my career and I know that it will be the same in Manchester. I cannot wait to experience the Old Trafford atmosphere when it is safe for the fans to return.