According to the Georgetown University Student Association Elections Commission, 2,541 students - 66 percent of voters - approved the measure while 1,304 students voted against it, according to CBS Voting ended Thursday night.
The fund would be the first of its kind in the country.
A "Reconciliation Contribution" fee of $27.20 (£21) each semester would go to descendants of the 272 slaves.
We value the engagement of our students and appreciate that they are making their voices heard and contributing to an important national conversation.
"There are many approaches that enable our community to respond to the legacies of slavery", Olson said. "The University has made a commitment to further our efforts in dialogue and partnership with the Descendant community, seeking to promote work that draws on the inherent strengths and expertise of our community in collaboration with the Descendant and Jesuit communities and that promotes racial justice", Todd Olson, Georgetown University's vice president for student affairs, said in a statement. The referendum isn't binding, however, and would still need to get the OK from the university's board of trustees.
Barack Obama, America's first African-American president, and 2016 Democratic nominee Hillary Clinton did not support the idea.
Several Democratic candidates for the White House, such as former Mayor Julian Castro, former Rep. Beto O'Rourke, and Senators Elizabeth Warren and Kirsten Gillibrand, have referred to the issue and have been in favor of some form of reparation.
Tuition at Georgetown, a private school in Washington, D.C., costs about $55,000 a year.
After the passage of the bill, Georgetown sophomore Eliza Dunni Phillips, a member of the GU272, told CNN: "The vestiges of slavery are still so evident, and so numerous African Americans whose ancestors were enslaved are still so disenfranchised".