Gunners boss Arsene Wenger confirmed this week the French midfielder had left to join the La Liga outfit, who have since unveiled Coquelin as their latest signing.
Arsenal are believed to have accepted a £12m offer for the 26-year-old, who has a £71.2m release clause in his Valencia contract.
Coquelin revealed he had quizzed his former Arsenal team-mates over the potential move, telling his new club's official website: "They [former Arsenal team-mates] all said that Valencia is a great city and a big club, so I am very happy to be here.
"I have seen the team, they are going along very well, they are third in the table. I have watched their recent games, since I knew that the negotiations between the two clubs were picking up, such as the Copa del Rey game versus Las Palmas. They were very good.
"I believe that the players are doing a great job. Obviously, I am here to help the team and to help them hit their targets."