The Spaniard moved across London on Thursday for a reported £4m fee and takes the Hammers' spending this summer close to £100m.
Perez wrote the farewell message on his official Twitter account, saying: "Today I would like to thank Arsenal fans for their support, they always showed me affection and love from the first time I arrived in London.
"I also want to give my thanks to my teammates and to the staff of this club for giving me the opportunity to make my debut in one of the best leagues in the world and win the FA Cup. I wish you all the best for the future and I hope you can go on and achieve great things."
Perez made the same move as former Gunners midfielder Jack Wilshere, who switched to the London Stadium earlier in the window.