The midlands club will pay £600,000 up front for the talented Irishman, with a further £250,000 if they win promotion to the Premier Division while Keogh is a player with them.
United will also receive 15 per cent of any transfer fee Wolves receive for the player.
"The Iron have reluctantly agreed to sell Keogh after the player expressed a desire to join the Championship side," read a statement from SUFC.
The Republic of Ireland U-21 international marked his final appearance for the club with a stunning solo go in Saturday's 2-2 draw with Doncaster.
It is the highest transfer fee United have ever received, surpassing the £350,000 - plus some seats for the away end at Glanford Park - which Aston Villa paid for defender Neil Cox in 1991.