It turns out Arsenal weren't that desperate to bring back Carlos Vela after all. Despite reports that Arsenal were ready to bring back the 25-year old Mexican, it turns out they were far more interested in the money he could bring, either through being sold by Real Sociedad, allowing Arsenal to get 50% of the fee, or by having his buy-back clause bought out by Sociedad. The latter has now happened.
Real Sociedad today announced that Vela has signed a new four-year contract; obviously, that scraps Arsenal's buy-back clause, for which Sociedad have reportedly paid Arsenal £8.8m, with the possibility of £4m in add-ons and a 20% sell-on clause. All told, this means Arsenal have gotten nearly £16m for the player since his move to Sociedad in 2011, originally on loan, which seems rather good negotiating from the club.
That's a decent amount of money, and will likely be used for wages and transfer fees in the near future; so while Vela won't contribute directly for Arsenal next season, he may have done his part.