Madsen flew to Utah on Sunday, where he is expected to meet with his new players on campus Sunday, sources said.
A formal announcement of Madsen's hiring is planned on Sunday, sources said.
Madsen, 43, has been a recognizable fixture on the West's basketball landscape for years, including as a member of two Lakers championship teams and later as an assistant coach under Byron Scott and Luke Walton.
Madsen's coaching career has included six seasons on the Lakers staff, a year as the Lakers G League head coach and a season as a college assistant at his alma mater, Stanford.
Madsen replaces Mark Pope at Utah Valley, which is a member of the Western Athletic Conference. Pope was hired at Brigham Young after a 25-win season at Utah Valley.
Madsen played nine seasons in the NBA, including his first three with the Lakers after selected 29th overall in the 2000 NBA draft. He was part of championships teams in 2001 and 2002, and he played his final six NBA seasons with the Minnesota Timberwolves (2003-09).
Madsen earned an MBA at Stanford's Graduate School of Business in 2012.