Monreal joined Arsenal from Malaga in January 2013 and went on to appear 250 times in all competitions, scoring 10 goals and winning three FA Cups and three Community Shield trophies.
The 33-year old is the second senior member of Arsenal’s back four from last season to depart the Emirates Stadium after former captain Laurent Koscielny forced a transfer to French Ligue 1 side Bordeaux.
Monreal has appeared in all three league games for Arsenal so far but Unai Emery will now have to choose between Sead Kolasinac and summer signing Kieran Tierney, who is nursing a groin injury, to fill the left-back slot.
Arsenal have been busy in the summer transfer window, bringing in Nicolas Pepe, David Luiz, Kieran Tierney, Danny Ceballos and William Saliba while Aaron Ramsey, Danny Welbeck, Laurent Koscielny and Petr Cech have all left the Emirates Stadium.
Arsenal released a statement confirming Monreal’s departure and thanked him for his services.
"We would like to thank Nacho for his contribution to the club and everyone at Arsenal wishes him the best for his future," read a statement from Arsenal.
"The transfer is subject to the completion of regulatory processes."
Real Sociedad meanwhile have confirmed the arrival of the 22-time capped Spain international.
"Real Sociedad and Arsenal FC have reached an agreement for the transfer of Nacho Monreal to the Txuri Urdin team. La Real, in turn, has reached an agreement with the player until June 30, 2021.
"The official presentation will be held on Monday, schedule to be confirmed."
