The striker has been at the Liga club since 2011 and Arsenal's buy-back option has been nullified with the player signing a four year deal.
The Mexican striker has been at the club since 2011, after spending a season on loan before joining on a permanent deal.
The Basque side bought him for 3 million euros in 2012 but the Gunners had a buy-back option which would see him return to London for only €4 million.
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After a good season in La Liga, reports began to circulate that the Premier League giant could activate the option, but Sociedad revealed on Tuesday that the two clubs have agreed a new deal which nullifies the clause and he has signed a new deal which ensures he remains in Spain for at least another four years.
"Real Sociedad have reached an agreement with Arsenal FC which will allow Carlos Vela to continue at the club on a permanent basis," a statement on the club's website read.
"The player meanwhile, has signed a contract extension which ties him to Real Sociedad for the next four seasons.
"The player's previous contract was due to expire in June 2016. The Mexican striker has now formally signed his new contract."