The Mexican striker still left the Emirates in 2011 for San Sebastian but the Spanish club have now agreed a deal with the Gunners which sees him grow to be their participant - with no strings.
A statement on the True Sociedad site read : " True Sociedad have achieved an settlement with Arsenal FC which will permit Carlos Vela to keep on at the club on a lasting foundation.
"The participant meanwhile, has signed a agreement extension which ties him to Real Sociedad for the upcoming four seasons. The player's past agreement was because of to expire in June 2016. The Mexican striker has now formally signed his new agreement."
Vela has made 126 appearances for True in formal competitions, scoring forty seven targets.
Vela explained : " I have also stated that this is my house, I am very nicely in San Sebastian, which is what I informed the president when he asked my about my intentions.
"We knew it would not be simple, but fortunately items have turned out nicely and all get-togethers are content.
"This club, this staff, have the ambition to have on increasing and I'm confident we are heading to have an exciting year. Now I'm going to enjoy the final several times of holiday break with my relatives and then be in a position to get ready for the season in the greatest vogue."
In the meantime, reports in Holland suggest that Sociedad are closing in on a offer for Icelandic forward Alfred Finnbogason.
Fulham had been believed to be in for the prolific frontman in January, but it would now seem as however the 25 - yr - outdated will be swapping existence in Holland at Heerenveen for that in Spain.