Fabianski was out of contract at the Emirates and rejected a new deal from the Gunners.
The Pole grew tired of being second-choice to younger rival Wojciech Szczesny and will now hope to make his mark at Swansea.
Fabianski becomes Swansea boss Garry Monk’s first signing since taking over from Michael Laudrup in February.
Arsene Wenger said he had wanted to keep the 29-year-old, who played a key role during Arsenal’s successful FA Cup run last season.
The move also puts the future of Dutch keeper Michael Vorm under threat amid reports he could head to Liverpool this summer.
Swansea stated on their website: “Swansea City is pleased to announce the club’s first summer signing with the arrival of goalkeeper Lukasz Fabianski from Arsenal.”