The England international has put pen to a four-year deal with the Baggies, where he will wear the number three shirt at the Hawthorns.
Gibbs spoke of his delight at joining West Brom, while also issuing a heartfelt farewell to the Gunners.
He posted on Twitter: “Delighted to have signed for @WBA.”
A statement attached to the post read: “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 an especially my team-mates 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.”
West Brom also confirmed the news on their official Twitter account, posting: