The school announced the move early Thursday morning and said it would hold an afternoon news conference to introduce Diaco.
Diaco, 40, takes over a team that went 3-9 this season. UConn fired Paul Pasqualoni after an 0-4 start and a 10-18 record in just more than two years at the school.
Notre Dame finished 8-4 this season
Diaco, who spent four seasons at Notre Dame, won the 2012 Broyles Award as the nation's top assistant coach, becoming the first Fighting Irish assistant to receive the honor.
Earlier on Wednesday, Michigan State defensive coordinator Pat Narduzzi, the 2013 Broyles winner, said he had withdrawn from consideration.
Diaco, from Cedar Grove, N.J., was the linebackers coach and special teams coordinator at Virginia. He spent the 2009 season as Cincinnati's defensive coordinator before moving to Notre Dame with head coach Brian Kelly.
Diaco is a 1995 Iowa graduate who began his coaching career in 1996-97 as a graduate assistant at his alma mater. He also served on the staffs at Western Illinois (1999-2000), Eastern Michigan (2001-2003) and Central Michigan (2005).
His 2012 Irish defense ranked second in major college football in scoring defense, allowing just under 13 points per game, and gave up only 15 offensive touchdowns.
Connecticut athletic director Warde Manuel began face-to-face interviews for the job Sunday, a day after UConn completed its season by routing Memphis 45-10, the Huskies' third consecutive win.
Interim coach T.J. Weist, who led the team to a 3-5 record after taking over for Pasqualoni, had made it clear he hoped to remain in the position.
But Manuel said the job had attracted an impressive pool of candidates. In addition to Diaco and Narduzzi, Ball State head coach Pete Lembo and Virginia Tech defensive coordinator Bud Foster also were linked to the position.
Manuel said he received input from important boosters and 25 former UConn players in narrowing down the finalists. He also said Saturday that money would not be an impediment to hiring a new coach.
Terms of the deal with Diaco were not immediately released. CBS, which first reported the hiring Thursday, said Diaco would receive a five-year deal worth about $1.5 million per year.
Manuel, a former Michigan defensive end, also noted that while 27 of 31 open jobs a year ago went to coaches with experience on the offensive side of the ball, he had no such bias.
"I'm equal opportunity," he joked. "With the exception of special teams coordinator. No offense to special teams coordinators."
Manuel also said the new coach will be allowed to choose his own staff, but as athletic director, he would have veto power over those choices.
He also said that while he will have some patience with the new coach, the job comes with expectations.
"This is being done so we can start winning next year, not four years from now," he said.