The 23-year-old has signed a three-year deal, with the Tigers having the option of a further year.
Kingsley, a Scotland international, made 17 Premier League appearances for the Swans after joining the club from Falkirk in June 2014.
After completing the move to the KCOM Stadium, he told the Hull site: "I'm delighted to get the deal done.
"It's come around quite quickly but I'm just delighted it's got over the line now and I can't wait to get training in the morning.
"It's time for me to really kick on now and get plenty of games at a very competitive level like the Championship."
Kingsley's move to Hull took place on the same day that midfielder Sam Clucas departed Humberside for Swansea.