The 28-year-old midfielder will sign a 3-year-deal once Ken Bates' buy-back offer for Leeds is confirmed by the Football League.
Simpson originally made a move for Nicholls in the January transfer-window and also tried to loan him towards the end of last season.
Nicholls began his career at Charlton and moved to Wigan via a loan spell at Brighton. He made his mark at Luton under Mike Newell and despite interest from a host of club's joined Leeds for £750k last summer.
He fell foul of the Leeds support however when he made known his desire to leave the club for a return to Luton after making only 15 outings.
Without doubt he's probably the worst captain Leeds have ever had and it's good riddance on our part.