He died this afternoon of a heart attack in Cairo," Mr Sharif's London-based agent Steve Kenis told news agency AFP, adding the actor had been in a hospital for patients with Alzheimer's disease.
Mr Sharif, and Egyptian of Lebanese descent, was born Michel Demitri Chalhoub in 1932. He studied mathematics and physics at the University of Cairo and eventually went to London's prestigious acting school RADA.
As Omar Sharif, he began his career in 1953 appearing in several Egyptian films. His breakout international role came with David Lean's 1962 classic Lawrence of Arabia, in which Mr Sharif played the tribal leader Sharif Ali opposite Peter O'Toole as T E Lawrence. His performance earned him an Oscar nomination and the Golden Globe for Best Supporting Actor.
Mr Sharif went on to star in David Lean's Doctor Zhivago. His body of work includes films such as McKenna's Gold, Che!, Funny Girl, The Pink Panther Strikes Again and Top Secret!
Omar Sharif was married to actress Faten Hamama, with who he had a son. They later divorced.
With inputs from AFP