The transfers leave coach Patrick Ewing and the Hoyas with just seven scholarship players.
Alexander and Gardner were two of three Hoyas facing accusations of harassment and burglary, stemming from separate complaints filed by two Georgetown students.
Alexander and Josh LeBlanc, who entered the NCAA transfer portal last week, both received restraining orders in November. The restraining orders were granted on Nov. 20, after the two players did not appear at a Nov. 14 hearing.
According to the Washington Post, a second complaint filed against LeBlanc, Alexander and Gardner was mutually resolved Monday without the admission of or finding of guilt. The complaint, which included allegations of sexual harassment and assault, was resolved when Gardner, Alexander and LeBlanc agreed to stay at least 50 feet away from the complainant.
Alexander announced his transfer via Twitter, while also declaring his innocence and blaming Georgetown for its lack of support over the past two weeks.
"I have been publicly shamed, threatened and criminalized," Alexander tweeted. "I have been falsely accused and targeted by the media and my peers of crimes I did not commit. My character has been defamed and that needs to be cleared up more [than] anything else. Very soon it will come to light that I am innocent and had nothing to do with the false allegations. ... In light of the situation, the University has allowed me to become a target and subjected to unfair treatment, with little or no support."
Gardner sent a statement to the Washington Post through his attorney announcing his decision to transfer.
Alexander, a 6-foot-6 junior who started his career at LSU, averaged 4.2 points and 2.7 rebounds in nine games this season. Gardner, a 6-6 freshman, averaged 3.1 points and 2.9 rebounds in eight games.
James Akinjo, the reigning Big East Freshman of the Year, is taking an official visit to Arizona this weekend, sources told ESPN.
ESPN 100 recruit Terrance Williams also decommitted from Georgetown last week after not signing a letter of intent during the early signing period.
The Hoyas (6-3) host Syracuse on Saturday.