The Uruguay international was rumoured to be ending his time in Manchester after just one season but he has now decided to stick around for one more year.
Cavani has scored 15 goals so far in his debut campaign in English football and earned plaudits for his attacking movement.
Confirming the news, the striker said: ‘Over the season, I have developed a great affection for the club and everything that it represents.
‘I feel a deep bond with my team-mates and the staff who work behind the scenes here.
‘They give me extra motivation every day and I know that, together, we can achieve special things.
‘From the very first moment that I arrived, I felt the confidence of the manager. As a player, this belief gives you the perfect opportunity to play your best football and I want to thank him for that.
‘I have been touched with how much the supporters have wanted me to stay, and I will give everything to bring them happiness and joy with my performances on the field.
‘I’ve not yet been able to play in front of the Old Trafford crowd and that is something that I cannot wait to do.‘