The 29-year-old signed for the Swans in May after spending seven years with Arsenal.
After rejoining the squad for pre-season training, the Poland international has made the effort to bond with his new teammates while on a two-week tour in the United States.
"The lads have been great with me as have the coaching staff and people behind the scenes," Fabianski told the club's official website. "It has allowed me to settle in very quickly at the club.
"Being in America is a big opportunity for me to get to know the players and staff because we are with each other 24 hours a day for two weeks. It's time to bond on and off the pith, and that is very important."
Fabianski will fight for his place with fellow goalkeeper Michel Vorm.