The Uruguayan, 34, penned a one year extension with United, keeping him at the club until 2022.
Asked about how Solskjaer influenced his decision to stay at United, Cavani told MUTV: "Talking about the relationship with the manager, I think that any influence he has had hasn't just been now at the moment of signing a new contract, but from the very first moment, even before I had signed, with conversations that I had with the manager.
"The way that he put his trust in me, the way that he made his feelings known about me and the confidence that he had with me, that was great from the word go. But over time and as the months have passed, the situation has just confirmed what I originally thought about Ole and that confidence that he gave me.
"Obviously, as time has gone on and games have passed by, he has made some really positive comments privately and in the media about me, as have my team-mates and the technical staff, the backroom staff, here, so that really, really helps as well.
"I think when you are a player, it gives you a huge amount of confidence when you know you have the backing of not only your manager but also other people around you. When you do get glowing comments about you, that is a real positive and is something that you are really grateful for."