The Welsh club confirmed the 29-year-old will join them on July 1, following the expiry of his Gunners deal.
The Poland international becomes Swansea boss Garry Monk's first signing since taking over from Michael Laudrup in February.
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."
Source : PA
Source: PA