Professor Ostriker, 64, who specialises in theoretical astrophysics, was a postgraduate fellow at the University of Cambridge in the 1960s before he joined Princeton.
Described as "an extremely lively and inventive astrophysicist" by Douglas Gough, head of the Institute of Astronomy, Professor Ostriker will bring new energy to cosmological research at the university.
Some Cambridge cosmologists believe that it will soon be possible to look back to the origin of the universe, perhaps by using the laws of physics to define their own starting point. Staff in the Institute of Astronomy will be collaborating with staff in the department of applied mathematics and theoretical physics and the Cavendish Laboratory on this and associated cosmological problems.
Professor Ostriker's professorship - created in 1704 - boasts an impressive history. Previous incumbents include Sir Arthur Eddington, who helped Einstein's theories gain acceptance through his measurements of the way that light was bent by the mass of the Sun during a 1919 eclipse. More recently, the chair was occupied by Sir Fred Hoyle, whose controversial theory that life originated in space gained some credibility with the recent discovery of possible signs of life in a Martian meteorite on Earth.
Professor Ostriker was awarded the United States National Medal of Science by the president last autumn. He has chaired the American Astronomical Society's committee on astronomy and public policy and served as a commission president for the International Astronomical Union.
Professor Ostriker's wife, poet Alicia Ostriker, professor of English at Rutgers University, will become a fellow of Clare Hall.