The 27-year-old full-back leaves the Emirates Stadium after a 13 years with the Gunners, coming through the ranks before going on to make 230 appearances for the first team.
Gibbs becomes West Brom’s sixth signing of the summer in a deal thought to be worth up to £7m.
“Firstly I would like to say how delighted I am to sign for West Brom. It has been an amazing journey to play for my childhood club since I was 14,” Gibbs wrote in a post on Twitter
“I would like to thank Arsene Wenger for giving me the chance to start my career and fulfil a dream. Thank you to all the fans, the Arsenal staff and especially my teammates who have been there during the special moments and have helped me through some tough times.
“Now it’s time for the next chapter with West Bromwich Albion and I can’t wait to get started with the boys.”
Gibbs could make his debut for West Brom against newly-promoted Brighton & Hove Albion after the international break.