Coquelin, who has signed a four-and-a-half-year contract with the high-flyers, revealed at his presentation that Los Che were interested in him last summer but he opted to stay with.
Valencia took advantage of the 26-year-old's lack of game time to swoop for the former France Under-21 worldwide, who will bolster their push for a top-four finish in La Liga. The club announced on its official site.
Speaking about Coquelin's move, he told Sky Sports: 'I'm happy for him because he's going to go to a team that is challenging at the minute in a very hard league to win.
Coquelin spoke to former Arsenal team-mates Shkodran Mustafi, Nacho Monreal, Hector Bellerin and Santi Cazorla about the move.
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He added: 'I've seen the team, they are doing very well, third in the table.
"We did think it was too good to be true", an Arsenal insider told FourFourTwo. "Obviously, I am here to help the team and to help them hit their targets".
The first player to officially leave Arsenal this January transfer window is not Alexis Sanchez, but Francis Coquelin.
He said: "I would sign him and I want him here permanently, but that's not my job".
"He goes to Valencia, he didn't get enough games", Wenger said following his side's 0-0 EFL Cup semi-final draw with Chelsea.