The 26-year-old, who joined the Gunners as a youth player in 2008, has signed a contract with the La Liga giants until 2022.
Coquelin was on Valencia's radar in the summer, but the Frenchman opted to stay at the Emirates Stadium to fight for a first-team place.
The gamble did not lead to more game time for the midfielder, however, with just one Premier League start and a total of 155 minutes of top-flight football under his belt.
"It's true that there was interest in the summer but in my head I wanted to continue at Arsenal and do well there," Coquelin told a press conference called to present him as a Valencia player. "It wasn't to be and now this opportunity has come up.
"I almost regret not having come before. I think it's an excellent opportunity for me and I'm very grateful. It's a big challenge, and a new start in my life for me, which I'm very excited about."
Coquelin, who signed a new deal at Arsenal a year ago, has made 105 Premier League appearances for the Gunners.