The defender has signed a deal with the Catalan giants to keep him at Camp Nou until 2025, with a reported salary of around €9 million.
Sport reports that Martinez will join Barcelona at the end of the season to bolster their defense.
His move to Barcelona follows the exit of veteran defender Gerard Pique and a series of injuries that have plagued the team.
Martinez, a Spain international, was close to joining Barcelona a few seasons ago.
Martinez was not Xavi’s preferred choice with the center-back position already well-covered.
Ref Watch: Manchester United defender Victor Lindelof's handball against West Ham 'a clear penalty'
Dermot Gallagher dissects the flashpoints from the weekend's action, including Manchester United defender Victor Lindelof's controversial handball incident against West Ham.
West Ham 1-0 Man Utd
INCIDENT: Let's start with the game at the London Stadium on Super Sunday. West Ham weren't awarded a penalty when Lindelof appeared to move his arm towards the ball in the box during the first half. Were you surprised this wasn't given?
DERMOT'S VERDICT: "Lindelof is extremely lucky. It should have been a penalty."
DERMOT SAYS: "I think he panics and moves his arm towards the ball. If a penalty was given he couldn't argue. The VAR decided it had hit him on the hand and the hand was in front of the body, so it wasn't outstretched. But what you would say is when you throw your arm like that and move it towards the ball, if you get punished you can't argue.
"The feedback from the PGMOL was that although his arm was out, it hit his hand and his hand was in front of his body, so they were of the opinion that he had focused on that, whether that's right or wrong I don't know.
"The handball rule is really tough. They felt his hand was in front of his body and wasn't making his body bigger, but I think because of the way he moved his arm towards the ball, that's what sold it to me that it should have been a penalty."
Stephen Warnock: "It's a clear penalty and you can understand why David Moyes and West Ham were so angry at the decision. The referee on the pitch should have been given the power to go over to the monitor and look at it again."
INCIDENT: VAR had another lengthy check over a challenge from Tyrell Malacia on Jarrod Bowen. It looked like the Manchester United left-back's studs caught the back of the West Ham forward's leg. Was a yellow card a fair punishment or should it have been red?
DERMOT'S VERDICT: "I thought it was a yellow card."
DERMOT SAYS: "It's not a nice tackle, he catches him. He's close and doesn't come from a great distance, so it doesn't gather speed. It's quickly down the back of his leg. It's not as if his foot is a long time going down it. I think the referee got that right."
Stephen Warnock: "Malacia knows what he's doing but a yellow card's the right decision."
INCIDENT: West Ham forward Michail Antonio thought he'd put the hosts 2-0 up but referee Peter Bankes deemed he'd fouled Manchester United goalkeeper David de Gea in the build-up. Was there enough in this?
DERMOT'S VERDICT: "It's a foul on the goalkeeper."
DERMOT SAYS: "Antonio knocked the goalkeeper's arm and stopped him from playing the ball. This is quite consistent with what we've seen across many seasons. You only have to knock the goalkeeper's arm a few inches and he's lost the ball and that's consistent with what we've seen, even in the seasons when I refereed.
"You've got to be very careful with the goalkeepers because they use their hands and if they get knocked a little bit, it makes a massive difference."