Cavani was instrumental as the Red Devils thrashed Roma 6-2 to take a giant step towards the final and Solskjaer was thrilled to see the striker making such a big impact.
The United boss said: "Edinson was excellent. I've said before, he plays as a centre-forward should be playing, running the channels, being the focal points, creating chances for others, scoring goals.
"He missed a couple of chances as well, but that is what he is there to do really, if he gets three or four chances a game, he will score two or three goals.
"I'm absolutely delighted with him. You can see the difference in him, he's worked up his fitness having had a long lay-off. He's making up for lost time."
It is unclear if Cavani will extend his stay at Old Trafford next season but Solskjaer is desperate to keep him at the club for a longer period.
He said: "Edinson was out for seven months and not playing football for a very long time before he came to us.
"He's had a couple of injuries and has worked really hard to show his quality.
"He knows my feelings, he knows that I would love to have him for another year, we have spoken about it. I understand this year has been very difficult, but I promised him that Old Trafford and Manchester is a different place with fans in the stadium.
"I'm doing my best, nights like this [help], hopefully we can get to the final and hopefully he can see himself being here for another year."