The midfielder has fallen down the pecking order at the Emirates and he has been linked with a move during the current transfer window. Valencia are on the lookout for a midfielder with a defensive mindset and Coquelin seems to fit the bill, given his experience and age.
Coquelin departs with FA Cup winners' medals for in 2015 and 2017 - and may be heading back to the Champions League.
Hammers coach David Moyes reveled in an interview earlier in December that he was searching for midfielders to add depth to his squad. Palace have found it hard in the league this season, but have been in good form since Roy Hodgson took over from Frank de Boer.
Loan spells at Lorient, Freiburg and Charlton followed before Coquelin broke into the Arsenal first team on a regular basis in the 2014/15 season.
Arsenal boss Arsene Wenger has confirmed that Francis Coquelin could leave the club this month with Valencia and several Premier League clubs interested in signing the French midfielder.