A buyout clause worth €80 million was inserted into the contract.
According to the Guardian's David Hytner, the transfer is valued at £12 million. The deal will run until June 30, 2022.
Coquelin joins a Valencia side that's surpassed expectations and sits third in La Liga, five points clear of last year's champion, Real Madrid, with 37 points after 18 matches.
Opportunities were few and far between this season in north London, as Coquelin primarily featured as a substitute for Arsenal in the Premier League.
Coquelin made a name for himself shortly after he was recalled in 2015 from his third loan spell, and it appeared as though he would carve out a permanent place in Arsene Wenger's team.
He featured in a career-high 29 league matches last term, but has been a surplus to requirements this season as Wenger has elected to deploy the resurgent Jack Wilshere, Granit Xhaka, and Aaron Ramsey in deep-lying positions in the middle of the park.