A police spokesman said employees at the Michelangelo hotel in Manhattan found the body of Mr Descoings, 53, on Tuesday afternoon.
Both the French president Nicolas Sarkozy, who studied at Sciences Po, and the Socialist presidential candidate François Hollande issued tributes to Mr Descoings.
Although a police source initially described the circumstances of the death as suspicious, investigators now say there is no evidence to suggest a crime was committed.
Mr Descoings’ stewardship of Sciences Po, which began in 1996, was associated with modernisation and internationalisation. The school also opened six campuses outside of Paris and raised tuition fees under his leadership.
In 2001, Sciences Po announced that it would drop entrance examinations for 10 per cent of its intake to recruit more poor students, a move known as the Priority Education Conventions scheme.
Mr Descoings attended private schools, graduated from Sciences Po and then the elite École Nationale d’Administration, worked in the Conseil d’État (France's highest administrative body) and advised Mr Sarkozy on secondary education reform in 2009.
In an interview with Times Higher Education in 2010, Mr Descoings discussed the need for wider-ranging methods of student assessment that looked at extracurricular qualities and talents, rather than relying solely on exam results or test scores.
In the interview, he said there was more to life than educational qualifications. “One day, I was looking through the death notices in the newspaper...they always begin with a name, a school and a graduation date. It would horrify me if my death notice in the paper began: ‘Sciences Po, Class of 1980’.
“I don’t want to educate young people to become cogs in the machine, or to use education as a status symbol. The important thing is to shape socially responsible students who can make positive contributions to their society.”
Mr Sarkozy said Mr Descoings gave underprivileged students the chance to study at the prestigious institution, marking “a historic turning point in awareness of scandalous social elitism in France”.
Jean-Claude Casanova, chairman of the Sciences Po board, said: “The death of Richard Descoings is an immense loss. Over the course of 16 years Richard Descoings has accomplished extraordinary feats which have profoundly transformed Sciences Po.”