Lingard, a United academy graduate, ended his 22-year association with the Old Trafford club following the expiry of his contract last month.
The 29-year-old England international, who made his United debut in 2014, scored 35 goals in more than 200 games for them.
Forest did not specify the length of his contract but Sky Sports reported he had signed a year-long deal.
He will wear the No. 10 jersey at Forest.