His royal palace announced Rainier's death nearly a month after he first was admitted to the hospital with a lung infection.
Rainier died at 6:35 a.m local time (12:35 a.m. EDT) at the Cardio-Thoracic Center. Prince Albert, his son and heir, was at his side. Rainier's doctors called Albert about half an hour earlier to tell him the end was near, the palace said.
A palace statement said Rainier died "as a result of the broncho-pulmonary, heart and kidney conditions that caused his hospitalization."
Flags, already lowered out of respect for Pope John Paul II, remained at half-staff. The two Monaco-based TV networks immediately interrupted programming with documentaries on Rainier's life and reactions to his death.
The mourning period could be fairly long, placing the funeral late next week, possibly Thursday, and making it unlikely to force another postponement of Britain's royal wedding between Prince Charles and Camilla Parker Bowles.
"Each of us feels like an orphan because the principality has been marked by his imprint over the 56 years" Rainier ruled the principality, said Patrick Leclercq, Monaco's head of government. While alive, Rainier was Europe's longest-serving monarch.
"Let us render, in dignity and respect, the immense homage that is his due for a body of work that resounded throughout the world and from which we reap the benefits," he said.
Rainier had suffered recurring health problems in recent years. The silver-haired, portly prince underwent heart surgery in 1999. In 2000, he had two operations, including having a nodule removed from a lung, and was hospitalized in 2002 for fatigue and bronchitis.
Recurrent chest infections put him in the hospital on numerous occasions thereafter.
French President Jacques Chirac said he learned of Rainier's death "with much emotion and great sadness."
Britain's Queen Elizabeth II, now the longest-serving monarch in Europe, also sent his family a message of condolence and was "saddened" to hear of his death, her palace said in a statement.
"With his entrepreneurial spirit, Prince Rainier played a decisive part in changing the principality in recent decades," German President Horst Koehler said in a telegram to Albert. "He fulfilled his duties as head of state with remarkable willpower until the end."
Rainier, from one of Europe's longest-ruling families, the Grimaldis, was a 26-year-old bachelor when he took the throne of the Mediterranean country nestled between Italy and the French Riviera in 1949.
His romance with Kelly captivated the world. She was a 25-year-old movie star when they met in 1955 at the Cannes Film Festival, and their marriage in 1956 put Monaco on the world stage.
Princess Caroline was born 10 months later, followed by Albert and Princess Stephanie.
Rainier never remarried after Princess Grace's death in a car accident in 1982.
Albert, who is unmarried, inherits a principality no larger than New York's Central Park but world-renowned for its casino and the annual Monte Carlo Grand Prix.
His father, after assuming the throne in 1949, had embarked on five decades of relentless expansion. Using landfill from the sea, Monaco expanded its territory by 20 percent.
Affectionately known as the "builder prince," Rainier oversaw the building of a whole new port, an artificial beach, a sparkling culture center and an underground railway station. A new breakwater project to allow large yachts and cruise liners to dock in the main harbor cost euro328 million.
Rainier could see his entire domain from the sandy-colored palace perched on a rocky cliff overlooking the sea.
However, Monaco has worked to overcome a reputation as a haven for questionable financial transactions.
It came under fire in 2000, and its relationship with Paris came under strain when a series of French official reports criticized its culture of banking secrecy and portrayed the principality as a shelter for drug barons, money-launderers and tax dodgers.