School vice president of athletics Paul Krebs announced the appointment Wednesday. Davie, who is a college football analyst for ESPN, will become the school's 31st coach.
He replaces Mike Locksley, who was fired in late September after going 2-26 in two-plus seasons.
Davie was head coach at Notre Dame from 1997 to 2001 and defensive coordinator with the Fighting Irish from 1994 to 1996.
He also has been defensive coordinator at Texas A&M and Tulane. In 1991, Davie's Texas A&M defense led the nation in total defense.
In Davie's first season, Notre Dame went to its first BCS bowl game -- the Fiesta Bowl. The Irish lost to Oregon State. Notre Dame played in two other bowl games under Davie.
He was fired in 2001 with a 35-25 record. He was succeeded by Tyrone Willingham, who was 21-15 in three seasons -- the same winning percentage as Davie. Charlie Weis, who followed Willingham, was 35-27 in five seasons.
Although his teams did well academically, the Irish, under Davie, were placed on NCAA probation for the first time as the result of a relationship between Irish players and a booster that started under then-coach and current ESPN college football analyst Lou Holtz and continued under Davie.
They also produced no first-team All-Americans and only one first-round draft pick, Luke Petitgout.
New Mexico officials declined to comment further on Davie's hiring.
The Lobos (1-9) got their first win of the season, and the third in as many years, last week by beating UNLV 21-14. They have two games remaining.
Locksley was fired mid-season after a nearly three-year tenure that was mostly marked by losses and off-field problems.
Locksley had been surrounded by controversy almost as soon as he became head coach, facing a sexual harassment suit, a suspension after he punched another coach, and -- the day before he was fired --
criticism after police arrested his son's friend on suspicion of driving while intoxicated in an SUV registered to Locksley's wife.
Associate head coach and defensive coordinator George Barlow has been serving as interim coach.
Joe Schad covers college football for ESPN. Information from The Associated Press was used in this report.