Davies having joined Liverpool from Championship side Preston North End will now be with the Blades for the remainder of the campaign.
The 26-year-old will be expecting to return to the top-flight with Sheffield United after the club was relegated from the Premier League last season.
Davies featured twice for the Reds during their pre-season and also came-off the bench at Anfield against CA Osasuna.
Celtic and Bournemouth were also keen on signing Davies, before his move to Anfield, while it is reported that one Premier League club made an enquiry too.
With the presence of Virgil van Dijk, Joe Gomez and Joel Matip all making their return from injury this summer, and new signing Ibrahima Konate, a first team opportunity looked impossible for Davies but a move to Sheffield United will guarantee him more playing time.
Reports are that Sheffield are also expected to complete the loan signing of ex-Leeds United midfielder Ronaldo Vieira from Sampdoria.
Having arrived in UK from Italy, Vieira completed his five days quarantine last week as he finished with his medical over the weekend.
Davies is expected to be in action when Sheffield play West Bromwich Albion on Wednesday as they hope to record their first win of the season after a goalless draw with Swansea in the season opener.
