Gibbs, who has 10 caps for the Three Lions, has signed a four-year contract at The Hawthorns.
Watford pulled out of a deal for the defender on Tuesday after failing to agree personal terms, despite agreeing a deal with the Gunners last week.
Gibbs lost his first-team place at Arsenal to Nacho Monreal last season when he made just eight Premier League starts and, having missed the pre-season tour to the Far East, has yet to feature this season.
The 27-year-old becomes the Baggies’ seventh signing of the summer, joining Jay Rodriguez, Zhang Yu’Ning, Ben Pierce, Ahmed Hegazi, Gareth Barry and Oliver Burke and brings the club’s summer spending to £38m.
Following the move, Gibbs posted an emotional farewell message to the staff and fans at Arsenal.
He thanked Arsene Wenger for giving him the opportunity to play for the club he supported as a boy while also stating how pleased he was to join the Baggies.
He wrote: “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. 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!”