But he suffered from injuries last season, limiting his playing time and affecting his ability to break through. This season he has made only 13 appearances, scoring three goals.
However, Gunners boss Arsene Wenger has high hopes for the left-footed forward, recently describing him as "great player", and in December 2009 Vela signed a long-term contract with the club.
Di Matteo added: "I'd like to officially welcome Carlos, who is an exciting signing for this club.
"There's no doubt that Carlos has the potential to become a great player and it will hopefully be a win-win situation, where we help him by giving him game time in the Premier League while he helps us achieve our goal.
"Having said all that, we have to remember he is still a young boy learning his trade and we will be giving him all the support he needs during his time here."
Vela has 29 Mexico caps, scoring nine times, and appeared at his first World Cup last summer in South Africa.
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