The 24-year-old midfielder, who joined the Hammers in 2014 after being released by Chelsea, has penned a long-term contract at the Emirates.
Arsenal announced the deal by live streaming a video of Rice being introduced to his teammates in a meeting.
Manager Mikel Arteta addressed his players during their pre-season tour of Germany before introducing Rice alongside fellow new signing Jurrien Timber, who was announced on Friday.
As the camera panned to Rice in the back row, he said: “I’ll say a few words. First day… really looking forward to playing with you all, to sharing memories together and see what you’ve been doing the last couple seasons.
“I’m really looking forward to getting started and enjoying a few trophies together.”
Rice, who will wear No.41, becomes Arsenal’s third signing of the summer and takes their spending to £210m.
In an official club statement, manager Mikel Arteta said: “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.