Dambrot received a seven-year contract, sources told ESPN.
"I am truly honored and blessed to be the head coach at Duquesne University," Dambrot said in a statement. "Today marks a new day for Duquesne basketball. We are here to build a program that our campus and community will embrace. We need to unite together. Everyone from our administration, faculty and staff, alums, students, and the Pittsburgh community will play a role in our success. I look forward to all the great things ahead for Duquesne."
Dambrot, 58, has been the head coach at Akron since 2004 -- and has taken the Zips to the NCAA tournament four times and to the NIT on five occasions.
Dambrot's departure was officially announced by Akron, which released a statement Monday night thanking him "for the enormous contributions'' and saying "we wish him well as he moves along.''
Dambrot will replace Jim Ferry, who was 60-97 in five seasons at Duquesne.
"From the moment we started this search, it was always about finding the right person and coach to lead our men's basketball program," Duquesne athletic director Dave Harper said in the statement. "Keith's combination of experience, leadership, and success is almost unmatched. We are blessed to have Keith leading our program. Beginning today, we will roll up our sleeves and purposefully work each day to ensure Duquesne is a highly valued member of the Atlantic 10 and target competing at the top of the conference in men's basketball."
Dambrot coached LeBron James during his first two seasons at Akron St. Vincent-St. Mary High School. After Cleveland lost to the San Antonio Spurs on Monday night, the Cavaliers star got the news that his former coach was leaving Akron.
"I support everything that Coach D do. He's paid more dues than any other coach in Akron history," James said. "He got a seven-year deal? He probably got a pay raise, too. He's going to have to take me to lunch when I get back."
Dambrot spent 13 seasons at Akron, compiling a 305-139 record. He has turned down other coaching jobs in the past to stay at Akron.
Akron said it will immediately launch a national search for a new coach.
ESPN's Ramona Shelburne and The Associated Press contributed to this report.