Coquelin, who first arrived at Arsenal as a 17-year-old in the summer of 2008 after a successful trial, has agreed a four-and-a-half year contract until June 2022.
The deal also comes with a cancellation/release clause of €80m.
A statement from Arsenal as the move was confirmed on Thursday afternoon read, "We wish Francis well at Valencia and thank him for his contribution to the club."
Having started in the youth ranks, Coquelin made his Arsenal debut in a League Cup tie against Sheffield United in the autumn of 2008.
A successful loan at Lorient in his native France followed during the 2010/11 campaign and the player started to feature more regularly for the Gunners over the next two seasons.
The 2013/14 campaign saw another foreign loan, this time to Freiburg in Germany, and his Gunners career looked to be petering out until an injury crisis resulted in Coquelin being recalled early from a loan at Charlton Athletic in December 2014 and thrust in to the team.
He played nearly every game for the remainder of the campaign, followed by 35 appearances in 2015/16 and 39 appearances in 2016/17. Coquelin has fallen down the pecking order this season, however, playing only 155 Premier League minutes in 2017/18 prior to leaving.
Shortly before the expected transfer was completed, Arsenal legend Thierry expressed surprise his fellow countryman has been allowed to leave the club.
The former France Under-21 international joins a Valencia side currently sitting third in La Liga with half of the season played, five points ahead of reigning champions Real Madrid and 11 points behind leaders and title favourites Barcelona.