Carvalho moves to the Bees for a £22.5m fee plus £5m in bonuses. Liverpool also retain a 17.5 per cent cut of any sell-on fee.
Bees manager Thomas Frank said: "Fábio is a player with a lot of qualities. He can play in all of the front three or four positions in a 4-3-3 or a 4-2-3-1. His best position is probably as a no.10 or coming in from the left.
"Offensively, he has great abilities on the ball: he can go past players, slide a pass, create chances and get on the end of chances. He's a type of player that we don't have many of in the squad so he will add that something extra for us.
"His ability and mentality to work hard in the pressure is also very, very good. That's along with him ticking all the boxes from a cultural perspective and being the right character. So we're very pleased to see him come in and push the team forward."
Carvalho also said: "It feels amazing, I'm so excited to be here. I've had a really warm welcome and I can’t thank everyone who has been involved in making this happen enough," Carvalho said in his first interview as a Bees player.
"I spoke to the manager and, from the first conversation that we had, I just knew I was going to come in and be excited about playing for the club, coming in every day and working with him.
"I just want to play football now and to do that in the best league in the world.
"As a player, you want to go somewhere where you’re wanted and somewhere where you’re loved - that's why I'm here.
"You want to be part of a family, part of a structure, and that's what Brentford is about. I'm just so happy to be here."