Sheffield United manager Neil Warnock told the club's website: "Jack has always been a player I admired and I have tried to sign him on numerous occasions."
Lester, who signed from Grimsby for £300,000, was a fan's favourite because of his grit and determination but his poor disiplinary record and lack of first-team opportunities meant that his contract was not renewed this summer.
Nottinghamforest-mad wishes Jack all the best at his new club.