"Arsenal Football Club is delighted to announce that Spain international Santi Cazorla has joined the club on a long-term contract," Arsenal said on their website on Tuesday.
Malaga, who are offloading players amid reports their Qatari owner wants to sell up, also confirmed the deal, which Spanish and British media reported was worth around 15 million pounds.
Cazorla is Arsenal's third major summer signing, joining Lukas Podolski and Olivier Giroud who moved from FC Cologne and Montpellier HSC respectively.
He said he had also discussed the move with some of the other Spanish players currently in the Premier League, including Chelsea pair Fernando Torres and Juan Mata, Manchester City's David Silva and Liverpool goalkeeper Pepe Reina.
"They have told me that it is great to play in the Premier League, they told me how the games are in England," Cazorla said on Arsenal's website.
"You see Spanish players doing well here and that inspires you to come over as well," he added.
"They have set an example and I hope I will adapt to the league as well as they have."
Fabregas, who returned to Barcelona last season, said he was delighted with the news of Cazorla's deal with his former club.
"I'm so happy to hear that my mate Santi Cazorla is finally a gooner," he wrote on his Twitter feed. "Top guy, special player. A great signing! Come onnn!"
Arsenal manager Arsene Wenger said Cazorla would add "significant quality" to the squad.
"He is a versatile, attacking midfield player who can play comfortably on either side of the pitch or centrally," Wenger told Arsenal's website.
"He has good pace, is technically gifted and will be a huge asset to Arsenal Football Club. We are delighted that he is joining us."
