Boss Arsene Wenger wanted to bolster his defensive options on the left-hand side, particularly in light of Kieran Gibbs' injury.
The 26-year-old has nine caps for Spain and joined Malaga on a five-year deal from Osasuna in 2011.
He will now link up again with former team-mate and compatriot Santi Cazorla, who made the same move in the summer.
Wenger, who is believed to have paid in the region of £8.5m for Monreal, told the club website: "We are delighted that Nacho Monreal has agreed to join us. We have been monitoring him for some time now and are really pleased that we've been able to agree this move today.
"Monreal is a strong left-sided defender with good experience at both club and international level.
"He is a technically gifted player, a good crosser in the final third and strong in the air. Monreal will add quality to our squad and of course, to our defensive unit. We all look forward to him playing for us."