Arsenal have confirmed that striker Carlos Vela has left to join Real Sociedad for an undisclosed fee.
The Mexican spent last season on loan with the Spanish side and scored 12 goals in 35 appearances.
The 23-year-old failed to establish himself in the starting XI at the Gunners and had further loan spells at Salamanca, Osasuna and West Brom.
Vela made 62 appearances for Arsenal since signing from Guadalajara for £550,000 in January 2006.