The Poland international, who has 21 caps for his country, arrives at the Liberty Stadium on a free transfer having spent the last seven years at Arsenal following a move from Legia Warsaw in his homeland.
Fabianski will officially become a Swansea player on July 1, when his contract at the Emirates Stadium expires.
The 29-year-old made just one Premier League appearance in the 2013-14 campaign, in a 2-0 win at Norwich City on the final day of the season.
His career with the London club ended on a high note, when he helped Arsene Wenger's side end their trophy drought by sealing a 3-2 extra-time win over Hull City in the FA Cup final earlier this month.
Fabianski will now provide competition for Gerhard Tremmel and Michel Vorm, although the latter has been linked with a move away from south Wales in recent weeks.
