Cech, who made over 400 appearances at Stamford Bridge and won the Champions League and four Premier League titles, joins Arsenal on a long-term contract for a fee British media reported to be worth around £11 million.
"I'm really excited about joining Arsenal and can't wait to join up for pre-season," Cech, 33, told the club's website.
"I have the same commitment to football, the same motivation and the same hunger for success as I had at the beginning of my career.
"When (Arsenal manager) Arsene Wenger spoke to me about his ambitions for this club, and how he saw me as part of this team, the decision was clear."
One of Cech's first games for Arsenal will be against Chelsea at Wembley on Aug. 2 in the traditional match between the FA Cup winners and Premier League champions.
Before that his new club play in the four-team Asia Trophy in Singapore next month and then host the Emirates Cup against Olympique Lyonnais, Villarreal and VfL Wolfsburg.
Chelsea were reluctant to sell the Cech but accepted he did not want to spend another campaign as deputy to Thibaut Courtois who is 10 years younger.
Belgian international Courtois became manager Jose Mourinho's first choice last season after returning from three years on loan at Atletico Madrid.
Cech moved to Stamford Bridge from Stade Rennes in 2004 but made only six appearances in last season's league triumph.
His other major honours included the Champions League in 2012, when he saved a penalty in the final against Bayern Munich and two more spot kicks in the shootout, the 2013 Europa League, four FA Cup wins and three League Cups.
"Petr Cech is a player that I have admired for a long time and I am very pleased that he has decided to join us," Arsenal boss Wenger said.
"He has proven over many seasons that he is one of the outstanding keepers in the world and he will add great strength to our squad."
