The 33-year-old completed his medical on Friday and has now signed a contract worth 100,000 pounds a week ($157,000), immediately making him one of the club's highest earners alongside Mesut Ozil and Alexis Sanchez.
The £11 million capture of Cech represents Arsenal's first signing of the summer, though Chelsea boss Jose Mourinho had been hugely reluctant to allow the veteran goalkeeper to join a rival.
Mourinho was keen to retain Cech as backup to Thibaut Courtois, but owner Roman Abramovich wanted to show respect for the Czech's 11 years of distinguished service so ceded to his wishes for first-team football as well as his desire to keep his young family in London.
Cech has played a key role in the most successful era of the Blues' history, winning four Premier League titles, the Champions League, Europa League, FA Cup and League Cup during his time at Stamford Bridge.
Despite being reduced to a bit-part role last season, Cech still showed his goalkeeping prowess by recording five clean sheets in his seven Premier League appearances.
His departure leaves Mourinho in need of a new shot-stopper to provide cover for Courtois, and the Blues have already identified Stoke City's Asmir Begovic as a primary target for the role.
Arsenal, meanwhile, is expected to sell Fenerbahce target David Ospina to make room for Cech, with Wojciech Szczesny to be his understudy, and the Czech could yet be followed to the Emirates Stadium by Chelsea goalkeeping coach Christophe Lollichon.