A formal agreement is expected soon and a news conference is possible as soon as Friday to introduce Crean in Athens, sources told ESPN.
The news comes one day after former Ohio State coach Thad Matta withdrew from the Georgia coach search after becoming the first known candidate to interview for the job.
Matta told ESPN, “I just don’t feel that I am completely ready at this point” to take the job.
Georgia fired Mark Fox on Saturday.
Crean, 51, spent nine seasons at Indiana before being let go after an 18-16 campaign in 2016-17. During his time in Bloomington, the Hoosiers went to four NCAA tournaments, reaching the Sweet 16 three times.
Crean also spent nine seasons at Marquette, reaching the Final Four in 2003 with a team led by Dwyane Wade. Crean made five NCAA tournament appearances with the Golden Eagles.
He also was an assistant coach under Ralph Willard for one season at Pittsburgh in 1994-95.
Georgia (18-15) lost to Kentucky in the quarterfinals of the SEC tournament, ending the Bulldogs’ hopes of landing a spot in the NCAA tournament.