The seven-year deal is worth an estimated $3.5 million per season, sources told ESPN.
"I am honored to be the head coach at Indiana University," Miller said Saturday in a statement. "IU is one of the greatest basketball programs and academic institutions in the country, and I cannot wait to get started. With peerless fan support, outstanding facilities and tradition, a beautiful campus, and located in one of the most fertile recruiting areas in the country, IU is a dream destination for me and my family."
Miller will replace Tom Crean, who was dismissed by the Hoosiers on March 16 after nine seasons. A news conference will be held Monday in Bloomington, Indiana.
"While there was great interest in this position, Archie Miller was on my short list from the very beginning," Indiana athletic director Fred Glass said in a statement. "The more I learned about him, the more convinced I became that he is the coach we need to meet our high expectations for many years to come.
"... Archie is a proven leader, proven winner, proven recruiter, and a proven player developer with a defense-first mentality that will help us win championships. Perhaps most importantly, he understands and embraces the special stature of Indiana University basketball and the critical relationship it must have with its former players, Indiana high school players and programs, and the entire State of Indiana."
The Hoosiers were 18-16 this season and failed to make the NCAA tournament for the second time in the past four years.
Miller, 38, guided the Flyers to a 24-8 record and the school's first outright Atlantic 10 regular-season title this year. He has spent the past six seasons with the Flyers and led the program to the NCAA tournament each of the past four years. He went to the Elite Eight in 2014.
"I want to extend our deepest gratitude and sincere thanks to Archie for an incredible run," Dayton athletic director Neil Sullivan said in a statement. "He is a first-class person and coach and has made incredible contributions to our men's basketball program, the university and the community. He has made a lasting impact on the student-athletes he has served."
Miller had a 139-63 record at Dayton, winning 24 games or more in each of the past four seasons.
"I want to thank all of the great people and players at the University of Dayton who have supported me along the way," Miller said.
Sources indicated Miller has long coveted the Ohio State job, where he was an assistant under Thad Matta from 2007 to 2009. However, Matta remains in Columbus, and Miller felt as though Indiana was too good of a job to pass up.
"We did everything we could to keep Archie at UD, but now our sole focus turns to continuing to build the quality of our nationally competitive program," Sullivan said.
Dayton said it would begin its search for a new coach immediately.
"We appreciate Archie's contributions in strengthening our program and returning it to national visibility," Dayton president Eric F. Spina said. "... This is a great basketball program in a great basketball town, and we will hire a great coach to build on that tradition."
Miller also worked as an assistant for his brother, Sean, at Arizona. In addition, he has been an assistant at Arizona State, his alma mater NC State and Western Kentucky. And he worked on the staff with USA Basketball's under-19 team, which won the FIBA world championship gold medal in 2015.
Miller's father, John, coached in high school. Sean, Archie and Lisa Miller all played Division I basketball.
The hire was met with approval by coaches throughout the college basketball landscape.
"I'm happy for him," said Butler coach Chris Holtmann. "It's a great spot for him.''
Said Notre Dame coach Mike Brey: "It's a great move for both."
"I was personally sad to lose Tom Crean, but I have always watched and respected the job Archie has done as an assistant and then the head coach at Dayton," Michigan State coach Tom Izzo said. "This league has some of the best coaches in the country, and it will be another great addition."
The Associated Press contributed to this report.