The 49-year-old, a lifelong Blades fan who has steered current club Port Vale to second place in npower League Two this season, will become the South Yorkshire club's third manager this season, Press Association Sport understands.
Adams will succeed Gary Speed, who left after only four months in charge at Bramall Lane to become Wales coach. Speed had been appointed following the sacking of Kevin Blackwell in August.
Vale are negotiating a compensation fee for Adams, who revived their fortunes during his 19-month stay at Vale Park.
Adams, released from the Blades youth team as a schoolboy, went on to enjoy a 19-year playing career as a left-back and had spells with Coventry, Leeds, Southampton and Fulham among other clubs.
He was appointed player-manager at Fulham in March 1996 with the club in the bottom division and led the Londoners to promotion the following season before being sacked by their new owner Mohamed Al-Fayed in 1997. Adams has since been manager at Swansea, Brentford, Brighton (twice), Coventry, Colchester and Port Vale.
Source: PA
Source: PA