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Sources also added that Arsenal will pay £45 million plus a further £10 million in add-ons to sign the striker, who will wear their No. 9 shirt.
"It's been a pleasure to play for Manchester City," Jesus said. "I feel like I am a better player now than when I arrived -- and to win 11 trophies has been amazing.
"My four Premier League titles are particularly special for me. I want to thank everyone at City -- the manager, my teammates and the fans -- for all the support they have given me over the past 5½ years."
As Arsenal boss Mikel Arteta added, "I'm very excited. The club has done a tremendous job to recruit a player of this stature. I know Gabriel personally very well, and we all know him well from his time in the Premier League and being really successful here.
"This is a position that's been on our radar for a long time now, and we have managed to get a player that we all wanted, so I'm really happy."
Jesus, who had only one year remaining on his contract at City, contributed 13 goals and 12 assists in all competitions for the Premier League champions last season, and the 25-year-old can play in all attacking positions.
In total, he scored 95 goals in 236 matches for City.