Kingsley penned a three-year contract at the Liberty Stadium on Monday after the two clubs agreed an undisclosed fee.
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He becomes Garry Monk's third new addition during the close-season, with Lukasz Fabianski and Bafetimbi Gomis having already agreed moves to the Premier League side.
Peter Houston, who was appointed Falkirk manager earlier in June, 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.
Fulton signed a new four-year deal on Monday and said: "Garry has been brilliant. He's put a lot of confidence in me and made me feel part of the squad and hopefully I can continue to progress under him."