Villa agreed a fee with the Glasgow side last night and the Spanish central defender agreed terms and passed a medical on Tuesday.
The 26-year-old told the club's website, avfc.co.uk: "I'm joining a big club in the Premier League.
"This is the best league in the world and last year Villa did very well. They play very good football and had a fantastic season.
"So I am very happy to come here with the opportunity to play in the Premier League. We are also playing in Europe this season, so that will be good.
"I watched Villa last season and Martin O'Neill is a very good coach. He plays exciting attacking football and I am excited to be here.
"My ambition is to play for my country and I think with Aston Villa I will have that possibility. Every player wants to play international football and that is my aim."
Villa boss O'Neill has been working hard to strengthen one of the smallest squads in the Premier League ahead of this weekend's opening fixtures.
Speaking before the deal was completed, O'Neill said: "We'll still have some players coming in to give us a chance and if we're lucky enough to qualify for the group stages of the UEFA Cup that would take us right up to Christmas and we'll most definitely need the squad.
"Last season we were exceptionally lucky with injuries. Eight or nine players played over 30 games and we didn't have big runs in the FA or League Cup - therefore we were able to concentrate on the league.
"All that could change this season and the fact is that we need the squad to be bigger to cope with that. That's what we're trying to do."