The deal also sees Joel Campbell join the La Liga side on loan for the remainder of the season, having agreed to a new long-term contract prior to the move.
Gabriel, 24, was an ever-present for Villarreal in the league this season prior to missing the weekend's 1-0 win over Levante ahead of his move to north London, helping the club concede just 17 goals in their first 19 games.
Also capable of filling in at either full-back spot, the former Vitoria defender is still to earn a call-up to the Brazil national team, but has been granted a work permit to complete his switch to the Emirates Stadium.
Speaking to the club's official website, the new Gunner said: “I came from a club that is not that big in Brazilian football. I went to Spanish football and that was another dream come true, to play in Europe.
"A while ago I had a really huge desire to play in the Premier League, so since that point I put it in my head that I really wanted to do it. I had a talk with my family and I told them that it was my dream to play in the Premier League. Getting here to such a big club is so gratifying.
“I am arriving at a big club and the fans can expect to find a Gabriel with a great will to help everyone," he continued. "Not just thinking of me as an individual, because to me that is not important.
"I care more about helping the team and my team-mates. I want to help everyone, so the fans can expect a Gabriel that on the field has a lot of will to be able to help the team win important things.”
While terms of the deal were not disclosed, it is believed that Arsenal have paid around £11.3 million for Gabriel's signature, per the Guardian, as Arsene Wenger bids to bolster his defence for the second half of the season.