Schmitt, who was elected to his largely ceremonial office in 2010 for a five-year term, said in a speech to Parliament's plenary session that he is stepping down because the controversy is dividing Hungary.
Schmitt, 69, then quickly left the chamber accompanied by Prime Minister Viktor Orban as lawmakers from the governing parties — Orban's Fidesz and the Christian Democrats — gave him a standing ovation.
The resignation comes at a turbulent time in Hungarian politics.
Last week, Schmitt's 1992 doctorate was revoked after a university committee, following up on a report published in January by the Internet publication HVG.hu, found that most of his thesis about the modern Olympic Games had been copied from the work of two other authors.
Schmitt had won two gold metals at the 1968 and 1972 Olympics on his country's fencing teams.
After Schmitt's speech Monday, Fidesz asked for a parliamentary recess so his party could arrange legislative votes needed to accept the resignation and choose a new president as soon as possible.
Schmitt's resignation came one day after he told state radio he would not step down.
However, pressure on him quickly grew, even among intellectuals and media close to Orban's government.
On Sunday, Tivadar Tulassay, the head of Semmelweis University, to which Schmitt's alma mater, the University of Physical Education, now belongs, resigned, saying he had supported the decision to revoke Schmitt's degree but lost the confidence of the Ministry of National Resources, which oversees educational affairs in Hungary.
For days, Orban had avoided the issue by saying the president enjoyed immunity and that only Schmitt himself could decide to resign.
During most of his speech Monday, Schmitt defended his doctorate and said he would appeal its revocation at the university and, if needed, in the courts.
"This is a matter of honor, and my conscience is clear," Schmitt said, adding that he was the victim of a political attack and that he would write a new doctoral dissertation about the relationship between sports and environmental protection, including the role of sports in sustainable development.
Schmitt has been a member of the International Olympic Committee since 1983. On Friday, the IOC said it will review reports related to Schmitt's case and decide whether any action is needed.