The 24-year-old centre back will undergo a medical with the London club on Monday before signing a deal.
He said goodbye to Villarreal fans ahead of their La Liga clash with Levante on Saturday, a tie Villarreal won 1-0.
"Villarreal CF and Arsenal FC have come to a preliminary agreement, that will be completed on Monday, for the transfer of Brazilian defender Gabriel Armando de Abreu," Villarreal said on their website.
"Once Gabriel passes the physical examination, he will join the Gunners in the Premier League."
The Brazilian, who can also play at full back, has played 50 times for the Spanish club. Media reports have said the fee is in the region of 20 million euros ($22.4 million), which is his buy-out clause.
Gabriel Paulista began his career with Brazilian side Vitoria, the same northeastern club where Bebeto, David Luiz and Dida started out, before signing for Villarreal at the beginning of last season for around three million euros.
He struggled during his first year in La Liga but has matured into a cultured centre half.
Campbell impressed on loan at Olympiakos in Greece last term and at the World Cup but the 22-year-old has failed to establish himself at Arsenal.
(Reporting by Tim Hanlon; Additional reporting by Andrew Downie; Editing by Mark Meadows/)
