Bent, 32, has been on loan at Wolves since August, but has made only five appearances for Mick McCarthy's side.
Blades manager Micky Adams was in charge of Bent during their time together at Leicester, where the forward spent the 2003/4 season on loan from Ipswich.
Bent will embark on his second spell at Bramall Lane, where he spent just over a year after arriving in a £300,000 deal from Port Vale in October 1999.
He scored 20 goals in 48 league starts for the Blades before previous manager Neil Warnock sold him to Premier League side Blackburn for £2.1million in November 2000.
Bent's previous clubs also include Brentford, Crystal Palace, Everton and Charlton.