Left-hander Mongia, 27, replaces Australian Brad Hodge who could be involved in the 2005 Ashes tour.
Mongia, who has a first class average of 53.29 and a career-best score of 308 not out, has hit 18 centuries and 20 half centuries in his total of 5,500 runs but has yet to play Test cricket for India.
But he has scored eight hundreds in limited overs cricket, including an unbeaten 159 for India, for whom he has played 48 one-day internationals. In all one-day competitions Mongia averages a healthy 34.34.
Mongia, also a useful left-arm spinner, gained experience of English conditions last season in two separate spells with Lancashire, first as a replacement for the injured Carl Hooper and then for Stuart Law.
In nine Championship innings he averaged 67.14 hitting two centuries and two half-centuries.
James Whitaker, Leicestershires Director of Cricket, said on Thursday: "We are delighted to have signed Dinesh Mongia as one of our overseas players in 2005. Dinesh is a high quality player who will offer the team exciting options with both bat and ball."
"With a very good record and an excellent attitude, we believe that he has the ability to contribute significantly on and off the field in 2005."
Whitaker also confirmed that Australian fast bowler Mark Cleary has agreed to spend another season at Leicestershire as their second overseas player after impressing last summer.