"It was mentally what I wanted to do," Monroe said in a statement released by the school Saturday. "I feel like I'm ready to make this step after working with our coaches for two years."
The 6-foot-11 Monroe was a third-team AP All-American as a sophomore after averaging 16.1 points, 9.6 rebounds, 3.8 assists and 1.5 blocks this season.
He was the Big East Conference rookie of the year in 2008-09 after averaging 12.7 points and 6.5 rebounds as a freshman.
"Greg and I, along with his family, have examined the situation, and he has made an educated decision," Hoyas coach John Thompson III said. "We have watched him grow as a player and as a young man while here at Georgetown. We support him and I look forward to watching and cheering him on for many years to come."
Monroe also was picked as the Pete Newell Big Man of the Year by the National Association of Basketball Coaches this season, when Georgetown went 23-11 and reached the Big East tournament final but was upset by Ohio in the first round of the NCAA tournament.
During his two seasons with the Hoyas, Monroe averaged 14.5 points and 8.2 rebounds.