The ex-Middlesex captain moved to Lord's from Essex in 2009 and has scored 5,977 first-class runs since making his debut for Kent in 2005.
Dexter, 31, has taken 28 wickets in all formats this season and is two scalps short of his 100th first-class wicket.
"It's a bit of a coup for the club," elite performance director Andrew McDonald told BBC Radio Leicester.
"It is nice to have someone of Dexter's experience, leadership qualities and skill set join the club.
"What he will offer in all three formats of the game is going to be superb. We felt that the little bit of extra experience was needed for this group to be the real deal next season.
"It is a good sign when players like Dexter approach us. It shows the steps forward we are taking on and off the field."
Leicestershire have signed Middlesex all-rounder Neil Dexter on a three-year contract from the start of next season.