ESPN 980 first reported the news.
Ewing, 54, was a former superstar center for the Hoyas before a long and successful NBA playing career, primarily with the New York Knicks.
Ewing reportedly will sign a multi-year deal, per Adrian Wojnarowski of The Vertical, and will take over as the team's head coach immediately, leaving his post as an assistant with the Charlotte Hornets. A press conference is expected for Wednesday, according to Jon Rothstein of CBS Sports.
Georgetown tweeted the following reaction to the breaking news:
The Hoyas fired John Thompson III in March after two consecutive losing seasons. He went 278-151 overall and made the Final Four in 2007. His father, John Thompson Jr., won a national championship as Georgetown's head coach in the 1983-84 season and reached the Final Four in two other seasons.
Georgetown pursued a number of big names to replace him, including Notre Dame's Mike Brey and Texas' Shaka Smart, Xavier's Chris Mack and Harvard's Tommy Amaker. Brey, Smart and Mack all turned down those offers, however, and Ewing ultimately emerged as the top candidate for the Hoyas.
Since his Hall of Fame playing career, Ewing has spent time as an assistant coach with the Washington Wizards, Houston Rockets, Orlando Magic and the Hornets.