The Gunners announced the move on their official website just as the deadline approached, saying they had paid an undisclosed fee for the 26-year-old.
The Spain left-back arrives at the Emirates Stadium at a perfect time for manager Arsene Wenger, who lost Kieran Gibbs for three weeks with a thigh injury on Wednesday night.
"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," Wenger said.
"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."