The 24-year-old, who was released by Aston Villa at the end of last season, has signed a two-year deal at the City Ground.
The American told the official Forest website: "I was disappointed not to play more games for Villa last season but that's in the past - I want to focus on my future with Forest.
"My agent told me just before the season ended that Forest were interested and it feels good to have finally signed - it's nerve-racking being a free agent and I'm very happy to come here.
"Hopefully I can help the team and the fans to take us back into the Premier League."
Lichaj, who began his career at Villa and made 23 appearances last season for the Midlands club, has experience of playing in the Championship courtesy of a loan spell with Leeds in the 2010/11 season.
"I know how the league is played and how the players are," he added. "I think I'll be able to adapt very well."