The Cooper Union for the Advancement of Science and Art, which is one of the last tuition-free colleges in the country but has been under severe financial strain, announced on Tuesday that for the first time in more than a century it will charge undergraduates to attend.

The decision ends almost two years of roiling debate about an education that was long revered for being “free as air and water,” and stood as the school’s most distinguishing feature, insulating it until now from concerns about the rising cost of a college degree.

Under the plan adopted by Cooper Union’s trustees, the prestigious college, based in the East Village, will continue need-blind admissions. But beginning in fall 2014, it will charge students based on what the college described as a steeply sliding scale, with those deemed able paying around $20,000, and many others, including those “with the greatest needs,” paying nothing. The change would not apply to undergraduates enrolled as of this fall.

“The time has come to set our institution on a path that will enable it to survive and thrive well into the future,” the board chairman, Mark Epstein, said in an announcement to students and faculty members in the college’s Great Hall. “Under the new policy, the Cooper Union will continue to adhere to the vision of Peter Cooper, who founded the institution specifically to provide a quality education to those who might not otherwise be able to afford it.”