The 29-year-old, who has 15 caps with the USA to his name, made the jump from Championship side to Championship side on a two-year deal, with the club holding the option for a third year.
Lichaj established himself as a regular with Forest, having made 190 appearances for the club since joining in the summer of 2013 from Aston Villa.
“I’m excited about playing here and I’m looking forward to getting started with pre-season next week," he said in a club release.
“It’s a fresh start for me and I want to repay Hull City for the faith that they have shown in me by bringing me here. I’ll be working my hardest, as I always do, every day in training and on matchdays.”
Lichaj was given his debut for the USA in 2010 but had his best year as an international in 2017, when he played in four matches and scored his first international goal in a 2-0 quarterfinal win over El Salvador in the Gold Cup.