Coquelin has joined the club from French third division side Laval.
The 17 year old impressed during a trial with Arsenal last season and had been expected to sign during the last two months.
He passed a medical back in May but his signing was only officially announced by the Gunners on Friday.
"Arsenal have signed French midfield player Francis Coquelin on professional terms," the club's official website announced.
"The 17-year-old has joined from SASP Stade Lavallois Mayeene MFC."