The Blades are in the Championship relegation zone after losing 11 of their opening 15 league matches and are the division's lowest scorers with just 11.
Manager Chris Wilder who took over the club just a few months ago has been in desperate need of attacking reinforcements and he looks to have got an experienced striker this week in Bamford.
As confirmed by the club, the 32-year-old has put pen to paper as he aims to lead the side out of the bottom three.
“United have added extra firepower to the forward ranks after securing a deal to sign an England international striker.
“Free agent Patrick Bamford has agreed a short-term contract until January with the Blades and brings with him a wealth of experience at Premier League and Championship level.”
Bamford has been a free agent ever since he was released by Leeds United in the summer after seven impressive seasons at Elland Road, during which time he netted 60 goals.
The striker was filmed leading Leeds fans in an anti-Wilder chant during promotion celebrations last season, but that incident now looks to be resolved as Wilder explained.
“I am a big boy, you give it, you take it. You give it out locally, you take it locally, as I have always done. We have our moments, other teams have their moments.
“I had a conversation with (Bamford) yesterday and I have no issue at all with it. I am not sure about the words used from a fellow pro, but I appreciate and respected him giving me a call, and we had 20 minutes.”