The midfielder has signed a four-and-a-half-year contract at Mestalla, which includes an $NZD132 million release clause.
Valencia is reported to have paid in the region of €$NZD22.3 million for the 26-year-old.
"Valencia have this Thursday reached an agreement with Arsenal for the transfer of Francis Coquelin," the club confirmed in a statement.
Arsenal manager Arsene Wenger revealed on Wednesday that a deal was likely to be concluded, with Coquelin having grown frustrated by his lack of game time.
"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.
"I let him go."
Coquelin has only made one start in the Premier League this season.