Cazorla, who was part of Spain's Euro 2012-winning squad earlier this summer, has moved to the Emirates Stadium after signing what Arsenal have called "a long-term contract".
The fee has also not been disclosed, but it is believed to be in the region of £17 million.
Arsenal manager Arsene Wenger told the club's official website: "Santi Cazorla is a great signing for us. He is a player with good experience at both club and international level, who will add significant quality to our squad.
"He is a versatile, attacking midfield player who can play comfortably on either side of the pitch or centrally. 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."
In his one season at La Rosaleda he scored nine league goals and set up another five to help the club finish fourth in La Liga, thereby qualifying for a Champions League.
The 27-year-old added: "I'm so happy to be joining Arsenal. This is a club with great players, a fantastic stadium and huge support.
"The club has one of the best managers in football and their style of play is recognised and admired all over the world.
"I'm so excited to be joining one of the greatest teams in Europe and also in the Premier League. I will do my best to help Arsenal challenge for trophies and make all the supporters happy."
Cazorla only signed for Malaga last summer from Villarreal, but the south-coast club has run into financial problems this summer and are expected to offload several other members of their expensively-assembled squad.
Venezuela striker Salomon Rondon had already left for Russian club Rubin Kazan before Cazorla completed his switch.