The 27-year-old England global has signed a four-year deal following his transfer from Arsenal for an undisclosed fee.
He's yet to feature in a match for Arsene Wenger this season, however, with the Arsenal manager shifting to a system in which he used three on the back line.
Gibbs made over 200 appearances for Arsenal during his time at the north London club and has also been capped by England at senior global level.
'It has been an awesome journey to play for my childhood club since I was 14.
A statement attached to the post read: "It has been an fantastic journey to play for my childhood club since I was 14".
The north London club have been linked with a move for West Brom's Jonny Evans, but he will not be part of any deal that takes Gibbs to the Hawthorns.
Arsenal are set for a busy end to the transfer window following their poor start to the Premier League season, as Arsene Wenger eyes a number of changes to his underperforming side.
'To add these qualities to our squad is exactly what we're looking for'.
Evans has now emerged as a prime target as the Telegraph claim that Arsenal approached West Brom on Monday night to discuss a deal for the Northern Ireland worldwide.