Davis, 28 signed for the Blades only twelve months ago from Preston North End for a fee of £2,500,000 but has been lured by the Premiership newcomers.
Derby County won promotion to the top flight after beating promotion favourites West Bromwich Albion 1-0 in the Play-Off Final at Wembley.
A statement on Derby's official website (www.dcfc.co.uk) read: "A £3million deal has been agreed with the strapping centre-half's club Sheffield United to make him the third signing of the closed season following on from Tyrone Mears and record capture Robert Earnshaw earlier this week.
"Subject to a medical and successful work permit application, the Jamaica international will sign a four-year contract with the Rams."
Davis joins the Pride Park club for a fee of £3,000,000 after making 19 appearances (+1) for the Bramall Lane club in his only season which ended in relegation from the Premiership.