The 22-year-old, who played 13 times for Arsenal last season and also had a loan spell at West Bromwich Albion from January, will play for the La Liga side subject to a medical.
Vela made his Arsenal debut at the start of the 2008/09 season having spent the previous campaign on loan at Spanish top flight side Osasuna while awaiting a work permit.
The promising forward, who started his career at Mexican club Guadalajara, played at the 2010 World Cup in South Africa.
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