He replaces Dave Calloway, who resigned under pressure. The Northeast Conference school plans to introduce Rice at a news conference Wednesday.
Rice, once a point guard who played for Dean Smith at North Carolina, has 13 seasons of college coaching experience, including 10 years working for current Vanderbilt coach Kevin Stallings.
Rice and Stallings were together for five seasons at Illinois State (1994-98) and the last five at Vanderbilt, which made the NCAA tournament four of the last five seasons.
"He brought a tremendous amount of energy, liveliness, hard work, and dedication to his position here at Vanderbilt, and I believe those attributes will make him a very successful head coach at Monmouth," Stallings said.
The 42-year-old Rice also worked at Providence and Oregon. He was the head coach of the Bahamas national team from 2001-04.
Rice played at North Carolina from 1988-91, helping the Tar Heels to a spot in the 1991 Final Four. He ranks third in assists on the school's career list.