The winner of two Golden Globe awards and an Oscar nomination for his role as Sherif Ali in David Lean's 1962 epic "Lawrence of Arabia", Sharif was known for his debonair style, raffish good looks and often mischievous joie de vivre.
He died in Cairo of a heart attack, his agent Steve Kenis said in London, after a struggle with Alzheimer's disease.
Close friend and Egypt's former antiquities minister Zahi Hawwas said Sharif died in an upmarket Cairo clinic where he had been under treatment for the past month.
"His psychological state had deteriorated, he wasn't eating or drinking," Hawwas told AFP.
Tributes poured in after the news of Sharif's death, with Hollywood star Antonio Banderas calling him "a great storyteller, a loyal friend and a wise spirit".
"I will always miss him. He was one of the best," he tweeted of the Egyptian star, who was fluent in six languages and also famous for his skills at playing the card game bridge.
Italian actress Claudia Cardinale, who acted with Sharif in Jacques Baratier's 1958 film "Goha," expressed her "great sadness" while renowned Egyptian actress Youssra said she felt "awful".
"I just lost (one) of the best people in my life, I feel so lost and unhappy and helpless," she told AFP.
The actor's grandson, Omar Sharif Jr, posted on Twitter: "I join my family in thanking everyone for the global outpouring of prayers and support we've been receiving. I will miss my grandfather dearly."
Propelled to stardom
Sharif began acting in the 1950s and his most high-profile roles were in the 1960s when he won an Oscar nomination for "Lawrence of Arabia" and Golden Globes for the same film and for "Doctor Zhivago".
His role in "Lawrence of Arabia" as Sharif Ali, an Arab chief enlisted by Peter O'Toole's T.E. Lawrence in Britain's fight against the Turks in World War I, propelled him to stardom, setting the stage for an even higher profile role in David Lean's subsequent release, "Doctor Zhivago".
Sharif played the hero in the epic adaptation of Boris Pasternak's novel of tortured passions during the Russian Revolution, with his real-life son Tarek playing his younger self.
The actor, fluent in Arabic, English, French, Greek, Italian and Spanish, went on to star in many films and television productions, including alongside Barbra Streisand in 1968's "Funny Girl".
"He was handsome, sophisticated and charming. He was a proud Egyptian," the American star said in a post on Facebook.
"I feel lucky to have had the opportunity to work with Omar, and I'm profoundly sad to hear of his passing."
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Sharif kept working over the following decades, often in television movies, and in later years became equally renowned for his prowess as a bridge player and owner of thoroughbred racehorses.
"I'd rather be playing bridge than making a bad movie," he once said, before announcing in 2006 that he had given up the game.
Sharif made something of a comeback in 2003 in the title role of the French film "Monsieur Ibrahim", playing an elderly Muslim shopkeeper.
The performance won him a best actor award at the Venice Film Festival and the best actor Cesar, France's equivalent of an Oscar.
Born Michel Demitri Shalhoub on April 10, 1932 in the Mediterranean city of Alexandria -- at the time a cosmopolitan hub -- to parents of Syrian and Lebanese extraction, he was raised a Catholic.
He studied at Alexandria's Victoria College before gaining a degree in mathematics and physics from Cairo University.
He joined his father's lumber business, but the acting bug had taken hold while he was studying, and in 1954 he made his silver screen debut in the Egyptian film "Siraa Fil-Wadi" ("The Blazing Sun") by Youssef Chahine.
The movie's romantic intrigue was echoed off screen as he married the leading lady, famed Egyptian actress Faten Hamama, converting to Islam and renaming himself Omar Sharif.
They had one son, Tarek, before divorcing in 1974. Hamama died in January 2015, with Sharif saying she was the only woman he had ever loved.
Sharif never remarried, but had another son, Robin, from a brief relationship with Italian journalist Lula De Luca.
He lived between France, Italy and the United States, before settling again in Egypt.
His playboy lifestyle of fine hotels, casinos and restaurants from California to the Cote d'Azur was not without its brushes with controversy.
In August 2003, he received a one-month sentence and a fine for headbutting a policeman outside a Paris casino. He was unrepentant, saying: "It made me the hero of the whole of France. To head-butt a cop is the dream of every Frenchman."
He was also ordered to take an anger management course by a California court in 2005, after punching a parking attendant.
Sharif had a triple heart bypass in 1992 and suffered a mild heart attack in 1994, according to the IMDb movie database website. The 100-cigarettes-a-day smoker quit after the operation.
In January 2011, during Egypt's popular uprising Sharif called for then president Hosni Mubarak to stand down, while at the same time expressing doubts about the Muslim Brotherhood.