The 24-year-old is thought to be keen to play in a central midfield role, while Blues manager Antonio Conte was reportedly keen to sign Oxlade-Chamberlain for a wing-back role.
The former Reds captain also suggested the 24-year-old decided on the move because he had become unhappy with life at his previous club.
Without a Premier League title in 13 years and absent from the Champions League this season following last term's fifth-place finish, Arsenal are no longer a marquee destination for the sport's top stars. He doesn't strengthen the team, but what he does do is strengthen the squad.
The loss of the midfielder will come as a big blow to Arsenal boss Arsene Wenger, who has been adamant in recent weeks that he wanted to keep the player at the Emirates Stadium.
The German described Oxlade-Chamberlain as a "positive" player who is "willing to take risks" and "has the mentality and desire to get even better".More news: Watch Jordan Vogt-Roberts' Destiny 2 Trailer
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"There's still Coutinho and Lallana to come back, players who performed so well".
"I watched the boys in the first few games of the season and they've got a lot of energy", Gibbs said in comments published on the West Brom website. He knows how many times after a game I've gone up to him after he's played really well and told him "Alex, don't you ever forget how good you could be".
Chamberlain was linked with Liverpool last winter, and also some 6 summers ago when he was newly coming through the ranks as an impressive teenager at Southampton.
"That's a brilliant deal to get". The youngster had scored 27 goals in 67 appearances for the Arsenal Academy.
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