The 27-year-old Wales international has signed a three-year contract with the League One club for an undisclosed fee.
Cullen joined Swansea’s academy at eight and went on to make more than 200 appearances after making his senior debut against Crystal Palace in the Carabao Cup in August 2018.
He scored five goals in 40 Championship appearances last season, with his final Swansea goal coming against Stoke City in March. Cullen also enjoyed a strong record in the South Wales derby.
"I am buzzing to be here and I can't wait to get started,” Cullen told Leicester City website.
"When this opportunity came about - and with the size of the club and the project they're getting started with now - I thought it was the perfect fit for me.
"The way we want to play football suits me really well. Keeping the football, playing in the opposition half, creating chances and scoring lots of goals."