The Mexico international, 23, scored 12 goals in 35 games as the Basque side finished 12th in La Liga.
And, having publicly declared his wish to stay in Spain, Vela looks set to return to San Sebastian for good.
“Carlos Vela is in San Sebastian this evening for final discussions about a permanent move to Spanish La Liga side Real Sociedad,” Arsenal confirmed in a statement.
“Further news will be issued [on the official website] in due course.”
The Spanish club said that the clubs had struck an "agreement in principle" over a four-year deal, and that any move would be finalised on Thursday.
Vela arrived at Arsenal as a 16-year-old from Mexican club Guadalajara but struggled to make an impact in the Premier League, only scoring five goals in 37 games for Arsenal and on loan at West Brom.
His record in Spain has been somewhat better, with eight goals and 15 assists while playing as a winger on loan at Salamanca, a slightly less successful spell at Osasuna and last season’s time at Real Sociedad, where his 12 goals and eight assists made for the best form of his career.
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