The Swans announced that left-back Kingsley, 19, had completed a medical and signed a three-year contract for an undisclosed fee.
Kingsley has made more than 100 appearances for the Bairns, making his senior debut as a 16-year-old, in addition to representing Scotland at Under-18 and Under-19 levels.
The young Scot was part of the squad beaten in a Championship play-off by Hamilton for the right to play Hibernian.
Kingsley will join fellow former Falkirk player Jay Fulton to the Liberty Stadium.
The 20-year-old midfielder made the move midway through last season and quickly impressed manager Garry Monk on the training ground and made his first Premier League appearance as a substitute in the 4-1 win over Aston Villa in April.
He made his first senior start in the final game of the season at Sunderland.