The French midfielder, 26, last played for Arsenal on 28 December in the 3-2 win at Crystal Palace where he came on as a second-half substitute.
Coquelin's departure could be the first of many for Arsenal during the January transfer window, with Alexis Sanchez, Theo Walcott and others looking for moves away from Emirates Stadium.
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"Valencia have this Thursday reached an agreement with Arsenal for the transfer of Francis Coquelin", the club confirmed in a statement.
Cancelo feels he hasn't been getting sufficient game time which could affect his chances of playing at the World Cup and he wants to return to Spain with Los Che also wanting him back. "If we ever see him again it'll be scoring an improbable but crucial goal against us in a Champions League clash".
'I think I was looking at it on TV yesterday, and they were saying who Arsenal can sign. "He is a defensive midfielder, basically", Wenger said after the game, as quoted by the Mirror.
Asked by Sky Sports after Arsenal drew 0-0 at Chelsea if Coquelin was about to leave Arsenal, Wenger replied: "Yes". "So that is as well as opening for him in midfield".