The 26-year old Spaniard has signed a long-term contract with the Gunners for an undisclosed fee.
"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," said manager Arsene Wenger.
"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."