Donald Graham said the "TheDream.US" fund already has raised about $25 million.
The program has other high-profile supporters such as the Bill and Melinda Gates Foundation, actor and director Diego Luno, former Florida Gov. Jeb Bush, and Grover Norquist, president of Americans for Tax Reform.
An estimated 65,000 students graduate from American high school each year without legal status. They don't qualify for federal financial aid or many other scholarship programs, and without financial assistance, their opportunities to go to college are limited.
A majority of states don't afford them in-state tuition, although a growing number of states are extending the opportunity.
Under the scholarship program, about 2,000 students are expected over the next decade to have their tuition, fees, and books paid for with the scholarship funds.
"All of us want to help set something right that is greatly wrong," Mr. Graham said at a press conference.
To qualify, the students must be participating in the "deferred action" program announced by President Barack Obama in 2012. That allows immigrants brought into the United States without legal permission as children to obtain temporary resident status for two years. The status is renewable.
Graham said he got involved with the issue after learning about immigrant students unable to go to college as part of his work with District of Columbia College Access Program. He said he didn't worry about wading into a political issue because "Educating kids is not taking a political stand," and he sees widespread bipartisan support for these students.
Last year, The Washington Post was sold to Amazon.com founder Jeff Bezos.
• To learn more visit http://thedream.us.