Bamford, who has one England cap, has signed a short-term deal with Sheffield United until January.
Bamford was filmed leading Leeds fans in a derogatory chant against Sheffield United manager Chris Wilder in April after Leeds secured promotion to the Premier League.
Wilder insisted he had “no issue” with Bamford’s behaviour and revealed the striker apologised to him over the phone.
Sheffield United are currently in the Championship relegation zone after losing 11 of their 15 leagues matches this season.