The 33-year-old goalkeeper has signed a long-term contract at The Emirates after passing his medical to end a transfer saga which has been drawn out over the last few months.
Cech, who has signed for an undisclosed fee, believed to be £10.9million, spent 11 seasons and made nearly 500 appearances with London rivals Chelsea.
He has been one of the mainstays of the Roman Abramovich era at Stamford Bridge, winning nearly every club honour with the Blues along the way.
Having been a regular for 10 years, he found his playing time limited last season, losing his first-team spot to Thibaut Courtois and had been expected to move on this summer, with Arsenal leading the chase for a couple of months.
The Czech star told the club’s website: “I’m really excited about joining Arsenal Football Club and can’t wait to join up for pre-season.
“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, and I love the challenges brought by the top quality players you face while playing in the Premier League.
“When 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.”
Gunners boss Arsene Wenger also revealed his delight at getting the experienced Cech on board.
“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.
“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,” he told Arsenal’s official website.