The deal was confirmed by the West Midlands club on their Twitter account:
In a bulletin on their website, the Baggies revealed Gibbs has agreed a four-year deal at the Hawthorns and will wear the No. 3 shirt.
Gibbs posted the following message on his own account:
The 27-year-old leaves Arsenal having spent 13 years at the club. Gibbs joined the Gunners youth setup in 2004, before going on to battle for the left-back slot in the senior side.
"I watched the boys in the first few games of the season and they've got a lot of energy," Gibbs said, per the West Brom website. "They've made some good signings and I feel this is a good move for me."
The England international had fallen down the pecking order at the Emirates Stadium, with Nacho Monreal taking over at left-back on a regular basis. The arrival of Sead Kolasinac in June meant minutes were even less likely to be on the cards for Gibbs this season.
West Brom will give the defender a chance to relaunch his career, and the Daily Mirror's John Cross believes Baggies boss Tony Pulis will be an ideal mentor for the ex-Arsenal man:
Gibbs will give West Brom something different, too. For long spells last term, the Baggies called upon makeshift options in the left-back position, with the likes of Jonny Evans and Chris Brunt deployed in that berth.
While Pulis sets his sides up to be defensively compact and a threat from set pieces, having a natural left-back in the squad will be a big boost to his side.
Gibbs may not be as combative as the players who have filled the position lately. What he will offer, though, is energy, tenacity and an appetite to get forward.
While it's a move that's unlikely to turn West Brom into a free-flowing attacking outfit, it's another savvy edition in a summer of real progress for Pulis' side.