The 16-year-old has not yet played for Chivas' first team but came to Arsenal's attention after scoring five goals in six games to help Mexico win the under-17 World Cup in Peru last month.
"It's official that Carlos Vela the under-17 world champion will belong to Arsenal Guadalajara said on their official website.
"We made three changes to his contract all of which were accepted by Arsenal said vice-president Nestor De La Torre.
"I asked what plans they had in mind for Carlos and they told me they were planning to loan him out to another side in order to develop him for playing in the Premier League but that's with Arsenal now.
"Vela's sporting rights will go to Arsenal for five years. If Arsenal decided to sell Carlos the first option would go to Chivas (Guadalajara)."
Vela could become only the second Mexican to play in the Premier League after the country's international striker Jared Borgetti who joined Bolton earlier this year.