West Ham were already interested but now West Brom have joined the race to sign him.
He was later loaned back to the Spanish side the following season.
Having been included in Arsenal's pre-season tour of Singapore it appeared Perez was potentially going to be given a fresh start under new head coach Unai Emery.
Perez joined Arsenal from Deportivo La Coruna in a reported £17.1m deal in August 2016 but failed to impress former boss Arsene Wenger, making only a handful of appearances during his two-year stint at the club.
The former Rayo Vallecano forward paid tribute to the Arsenal supporters in a message on his Twitter account, saying: "They always showed me affection and love from the first time I arrived in London".
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"I wish you all the best for the future and I hope you can go on and achieve great things".
Perez, 29, is the London club's eighth signing of the summer joining Ryan Fredericks, Lukasz Fabianski, Issa Diop, Jack Wilshere, Aindriy Yarmolenko, Fabian Balbuena and Felipe Anderson in completing the move to the London Stadium.
Chicharito added: "The manager called me before the World Cup because he knew my situation was hard at the end of last season, and he made me feel very good".
West Ham also sold one player on deadline day, shipping 18-year-old Portuguese midfielder Domingos Quina to Watford.