The midfielder has signed a four-and-a-half-year contract at Mestalla, which includes an €80 million (A$122.04 million) release clause.
Coquelin spoke to former Arsenal team-mates Shkodran Mustafi, Nacho Monreal, Hector Bellerin and Santi Cazorla about the move.
According to reports, Crystal Palace have joined a host of clubs ready to snap up Francis Coquelin from Arsenal.
After previous loan spells at Lorient and Freiburg, he came back from Charlton in 2014 and briefly looked the enforcer Arsene Wenger was missing.
"I think there are situations where you have doubt about these and you have to check but at the same time in extra time you have to consider this".
There is still much speculation about the long term future of German worldwide Mesut Ozil, although he is one of many that remain unsettled ranging from; Alexis Sanchez, Francis Coquelin, Theo Walcott and Mathieu Debuchy.