Rice has signed a five-year contract at the Emirates Stadium with the option for a further year.
The 24-year-old is Arsenal's third summer signing after Kai Havertz and Jurrien Timber.
Rice has also become Arsenal's record signing, eclipsing the £72m paid to sign Nicolas Pepe from Lille in 2019.
Rice has been handed the number 41 jersey at his new club.
Speaking to the Arsenal website, Rice said: "In football, amazing opportunities arise. Big clubs, like Arsenal, have come for me and it's really hard to turn down."
"You only ever get one career and I really believe in what Mikel is building here and the squad he's building. I'm really looking forward to the future with Arsenal.
"With Mikel and how he works, the squad, how young everyone is, the energy around the club and also the challenge of getting Arsenal back to where they belong, that means a lot to me.
"I know the fans really want that. For me as a player, I've come here really hungry to have more success and to spend my best years at this great club.
Arsenal manager Mikel Arteta added: "We're really happy that Declan is joining us. He is a player with tremendous ability, who has been performing at a high level in the Premier League and for England for a number of seasons now.
"Declan is bringing undoubted quality to the club and he is an exceptional talent who has the potential to be very successful here.
"Declan has great experience in the Premier League at only 24 years old. He has captained a very good West Ham team and as we all saw, he recently lifted a European trophy.
"The responsibility and role he has taken on has been very impressive and we are really excited that he is joining us."
