Kingsley penned a three-year contract at the Liberty Stadium on Monday after the two clubs agreed an undisclosed fee.
The 19-year-old defender has ended a nine-year association with the Scottish Championship side, which saw him make 108 appearances after breaking into the first-team in 2011.
He becomes Garry Monk's third new addition during the close-season, with Lukasz Fabianski and Bafetimbi Gomis previously agreeing moves to the Premier League side.
Peter Houston, who was appointed Falkirk manager earlier this month, told his club's official website: "Whilst I'm sad to see him leave, it is a wonderful opportunity for Stephen to progress his career.
"We all wish him the best of luck."
Kingsley is the second player to swap the Falkirk Community Stadium for Swansea in the last year, after Jay Fulton made the same switch in January.
