The 19-year-old defender has agreed a three-year contract at the Liberty Stadium for an undisclosed fee.
He told the club's website: "I know a lot about Swansea and, of course, Jay [Fulton, who joined from Falkirk in January] has been telling a lot of good things about the club too.
"To see Jay make his debut in the Premier League shows that the manager is not afraid to give youngsters a chance, and that's one of the reasons why I decided to come to Swansea.
"It has been a real education at Falkirk, but I feel I am now ready to take the next step in my career, and to be at a Premier League club is a dream come true for me."
Kingsley has made over 100 appearances for the Scottish Championship side since making his senior debut as a 16-year-old.