He replaces John Thompson III, the son of Ewing's former coach with the Hoyas, John Thompson Jr. A news conference is scheduled for 11 a.m. Wednesday.
"My four years at Georgetown were the best of my life," Ewing said in a statement released by the school. "Georgetown is my home and it is a great honor for me to return to my alma mater and serve as the next head coach. I have been preparing to be a head coach for many years and can't wait to return to the Hilltop."
Ewing, who has been the associate head coach of the NBA's Charlotte Hornets, met Monday with Georgetown officials.
"To hire a head coach with this depth of coaching experience and personal achievements is tremendous,'' athletic director Lee Reed said in the statement. "It is a thrill to have him come back to his alma mater and continue the legacy of tradition and success he had as a student-athlete on the Hilltop.''
The Hornets play Tuesday night in Washington against the Wizards, affording Ewing the chance to meet directly with Georgetown.
"This is a big loss for the Charlotte Hornets, but we are all excited for Patrick to have the opportunity to go back to Georgetown. Everyone knows how much his alma mater means to him," Hornets coach Steve Clifford said in a statement. "I've had the privilege of working with him for 12 years with three organizations and I know the effort he has put into coaching. He has attacked this profession with the same mentality he had as a player, with hard work, dedication and a passion for the game of basketball.
"I'm thrilled that all of Patrick's hard work has paid off and he has earned the opportunity to be Georgetown's head coach. We wish him the best of luck in the next chapter of his coaching career."
Ewing was the preferred choice of Thompson Jr.
Ewing is a Georgetown legend who played for the elder Thompson from 1982 to '85, guiding the program to three national championship game appearances and one title. He went on to have a Hall of Fame career in the NBA, playing 15 of his 17 years in the pros with the New York Knicks. Ewing is also a two-time Olympic gold medalist.
"Of all the players that have gone from superstardom to putting in the time and paying their dues to becoming a head coach, Patrick deserves this probably more than any player ever,'' said Miami Heat president Pat Riley, who coached Ewing with the Knicks. "I am absolutely delighted for him and I think he'll do a great job at Georgetown. Patrick Ewing was the first. He has come home.''
Georgetown fired Thompson III on March 23. He spent the past 13 seasons as the Hoyas' coach, going 278-151 with eight NCAA tournament appearances. Georgetown finished 14-18 this season, including a 5-13 mark in Big East play.
ESPN's Marc Stein, ESPN Stats & Information and The Associated Press contributed to this report.