CBSSports.com reported that the deal starts at $1.5 million per year.
The 40-year-old Diaco, the recipient of the Frank Broyles Award in 2012 as the nation's top assistant, coached a Notre Dame defense that finished second nationally in scoring during its run to the national title game that season, surrendering less than 13 points per contest and giving up only 15 offensive touchdowns. Diaco will be introduced as Huskies coach at a news conference at 3:30 p.m. ET Thursday.
The Cedar Grove, N.J., native has drawn plenty of attention the past two years for his work with the Irish, including interviewing for the Boston College head-coaching job last year. He was highly popular with his Notre Dame players, many of whom took to Twitter on Wednesday night to voice their frustrations when news of his reported departure broke.
Diaco spent the past four seasons leading the Fighting Irish's defense. In 2009, he was defensive coordinator at Cincinnati before moving to Notre Dame with head coach Brian Kelly.
With Diaco gone, and with offensive coordinator Chuck Martin taking the Miami (Ohio) job, Kelly now must replace both coordinators.
Earlier Wednesday, Michigan State defensive coordinator Pat Narduzzi, the 2013 Broyles winner, said he had withdrawn from consideration for the Huskies' job.
UConn fired Paul Pasqualoni in September after an 0-4 start and a 10-18 record in two-plus seasons at the school.
Connecticut athletic director Warde Manuel began face-to-face interviews for the job Sunday, a day after UConn (3-9) 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 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.
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."
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.
Information from ESPN's Brett McMurphy, ESPN.com's Matt Fortuna and The Associated Press was used in this report.