The Uruguay international, 33, who left PSG in June, has signed a one year contract with Man Utd.
One of his first United games could be against PSG in the Champions League group match on 20 October.
“Manchester United is one of the greatest clubs in the world, so it is a real honour to be here,” said Cavani. “I’ve worked really hard during the time off and I feel eager to compete and represent this incredible club.
“I look forward to continuing to write my little story inside the book of football and I know that’s why my focus has to remain the same as always – work, work, work. I have had a conversation with the manager and this has increased my desire to wear this beautiful shirt.”