Brown, 24 joins the Blades after the transfer deadline has ended with the defender being without a club, having being released by League One rivals Bury in the summer.
The younger brother of Wes Brown, who this week completed a move to Blackburn Rovers, will be eligible for Sheffield United's trip to table toppers Scunthorpe United today.
He had spent a short time at Shirecliffe on trial before putting pen to paper on a short term deal until January 2017.
Blades boss Chris Wilder told sufc.co.uk; "He comes in and gives us cover at right-back or right wing-back. "He adds weight to our squad and knows the division well. He has done everything we have asked of him, trained well and impressed. "His pedigree is good and this is an opportunity to earn a longer deal."