Davies will move from Stoke City to Bramall Lane, becoming the Blades first signing of the January transfer window, again linking up with manager Paul Heckingbottom with whom the goalkeeper worked under at Barnsley.
The Wales international will come in and challenge for a starting place in the United goal following the departure of loanee Robin Olsen to Aston Villa.
Wes Fodderingham is the current number one, having taken the spot when Olsen picked up an injury on internatioanl duty with Sweden.
Stoke City boss Michael O’Neill has revealed the reasons why he was prepared to let Davies, who hasn’t played since the beginning of this month, leave the Bet365 Stadium and join a potential promotion rival.
The former Northern Ireland manager admitted he felt there was enough cover in the position and took into acount the fact that Davies’ contract runs out in the summer.
He told Stoke Sentinel: “It is not really a decision that has been taken as a reflection on Adam, it is more so the situation we are in with Joe Bursik getting closer to fitness.
“We feel that Joe has real potential to cement himself as the number one here, although I have been pleased with Jack’s [Bonham] contribution recently too.
“We also have Frank Fielding in the building contracted to us until the end of the month, so there is the option to extend that arrangement too.
“Given the level of finance in the deal with Adam, who is not really playing for us, is maybe better utilised in other areas."
“We had to make a decision with Adam. He’s out of contract at the end of the season,” O’Neill added. “He was keen to move and we had to make a decision based on finances.
"He’s not in our team and we had to put that money to better use in terms of where our squad is at this moment in time. That’s what we did."
United should announce Davies’ arrival on Monday, turning the focus towards signing a central defender before next week’s deadline.