The Togo striker, who takes City's summer spending to around £80m, passed a medical on Saturday and had already been successful in arranging a work permit.
Adebayor, who was also linked with linked to AC Milan and Chelsea, spent three-and-a-half seasons with the Gunners after joining them from Monaco for £7m, scoring 62 goals in 142 games.
He scored 30 goals in the 2007-08 season but struggled with injuries in the last campaign and also incurred the wrath of some Arsenal fans, who felt the striker lacked commitment.
Arsenal boss Arsene Wenger said he was sorry to see Adebayor leave, but insisted he had no immediate plans to replace him.
"We're not on the verge of signing anybody but I'm able to spend the money if we find the right players," he said,
"We have Tomas Rosicky and Eduardo back so we've lost a big striker but have gained two offensive players who were absent last season.
"We also have Nicklas Bendtner, Andrey Arshavin, Robin van Persie and Theo Walcott who can play striker. We have top players we can use as strikers.
"But we'll miss Emmanuel - he's a great player. I'm sure he'll give something special to Man City.
He adds vital balance and power to our attack - he has everything a top forward needs.
City boss Mark Hughes
"If you consider the money we paid for him it was good business, but that was not our main target."
City boss Mark Hughes said Adebayor's arrival was a major step forward for the club.
"Emmanuel has been one of the top forwards in the Premier League since he arrived from France and we are delighted he has agreed to come and join us," he said.
"Along with the other signings we have made in the last two windows he will greatly enhance our ability to compete with the top sides.
"His arrival is another clear indication that we are determined to augment the players we have here with the best of international talent.
"He adds vital balance and power to our attack. He has everything a top forward needs. He is versatile, powerful, quick and agile on the ball.
"I am looking forward to working with him as are the rest of the staff. He will definitely add a new dimension to our play. I have been a great admirer for a long time."
City, backed up the huge financial wealth of their owners, the Abu Dhabi United group, are eager to break into the Premier League's top four this coming season and have shown their determination with their close-season spending.
Midfielder Gareth Barry was bought from Aston Villa for £12m and City paid Blackburn about £18m for Paraguay international Santa Cruz.
City completed a deal for Tevez on Tuesday, with the Argentine joining after City paid a fee of about £25m to secure his registration from third party ownership after his contract with Premier League champions Manchester United expired.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.