The Frenchman parted company with the north London club after nine years service this January transfer window, for pastures new in Spain.
Valencia announced the 26-year-old signed a four-and-a-half year contract with a massive £71million release clause, which will keep him at the club until 2023.
Coquelin made 160 first team appearances for the Gunners, and lifted the FA Cup with the club in 2015 and 2017.
Addressing the club’s supporters in an emotional message published on Arsenal’s official website, the Frenchman said: “I just want to thank them.
“I was at the club for a very long time. I always showed passion for the club and they all saw that in me, so I want to thank them for their support.
“I understand what they feel – their love for the club, I understand that. I was at Arsenal for nine years and it was like a second family to me.
“I understand the frustration when the results are not going well.
“We had an honest relationship and the fans have always been amazing towards me. It’s been great.”
Coquelin joined Arsenal from French side Laval in 2008, and has fond memories of first agreeing terms with the Premier League giants.
“Coming to Arsenal at such a young age, from a small club, it was a massive step for me,” the Frenchman admitted.
“I would say that Arsenal raised me as a player, but also raised me as a man. I owe a lot to Arsenal, it has been nine years of my life and I will never forget it.
“But obviously I am moving on to a new challenge, a new club and my first impressions are very good so I am expecting another really good time.”