However, the club did not reveal how much they paid for the 27-year-old, but reports on British media put the fee at around £7 million ($9 million, 7.6 million euros).
The England international came through the youth ranks of The Gunners but having played regularly between 2012 and 2015, he subsequently found himself on the fringes of the first team.
Gibbs told West Brom’s website, “I watched the boys in the first few games of the season and they’ve got a lot of energy.
“They’ve made some good signings and I feel this is a good move for me.”
Confirming the deal, West Brom manager, Tony Pulis, said on their website, “Kieran’s a good age and has made over 200 appearances for Arsenal, represented his country and has Premier League and Champions League experience.
“To add these qualities to our squad is exactly what we’re looking for.”
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