Villarreal stated on Saturday that a deal to take centre-back Gabriel to Arsenal had been agreed in principle, and Arsene Wenger revealed on Sunday that the move would likely be sealed in the next 24 hours.
Gabriel, who can also play as a full-back, has now been granted a work permit and his move to the London club was confirmed on Wednesday.
The 24-year-old Brazilian told the club's official website: "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. 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."
Costa Rica striker Campbell is set to join Villarreal on loan for the rest of the season after agreeing terms on a new contract with the London club.
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