The former striker coached the Manchester City captain during his time as the assistant manager for the Belgium national team.
Henry told Sky Sports: "Listen, he's a thinker. You can talk about Vincent Kompany for days for what he has done for this football club and what he did on the field.
"What I would like to say is he is a thinker. I was in charge of the offensive corner for the national team and he used to grab me in the morning. Usually, when Vincent Kompany grabs you, it's for two hours.
"You're going to talk about it, you're going to look at the videos and he's going to tell me what we're supposed to be doing and it worked, to be fair, against Brazil.
"That's why, well he didn't touch the ball, but his run disturbed Fernandinho and he came to see me on the bench because in the morning he had chewed my head off on what we were supposed to do.
"He's a thinker, he loves the game, that's all he talks about. I love the man, I love the man he is off the field and the player he was here, obviously, because he hasn't stopped his career yet!
"What a player he was for this football club."