Shriver, who was diagnosed with Alzheimer's disease in 2003, had been hospitalized at Suburban Hospital in Bethesda, Md.
His death was eulogized by President Barack Obama as "one of the brightest lights of the greatest generation."
"Over the course of his long and distinguished career, Sarge came to embody the idea of public service," Obama said. "Of his many enduring contributions, he will perhaps best be remembered as the founding director of the Peace Corps, helping make it possible for generations of Americans to serve as ambassadors of goodwill abroad.
"His loss will be felt in all of the communities around the world that have been touched by Peace Corps volunteers over the past half century and all of the lives that have been made better by his efforts to address inequality and injustice here at home."
Besides being a driving force behind the Peace Corps, Shriver also was the first director of the Office of Economic Opportunity and served as ambassador to France.
He wound up on the ballot in 1972 as the Democratic nominee for vice president after Thomas Eagleton withdrew as George McGovern's running mate after it was revealed he had been treated for mental health issues.
In 1976 he declared himself a candidate for president of the United States but withdrew after making a poor showing in four state primaries.
Shriver became part of the Kennedy political family in 1953 when he married Eunice Kennedy, who died in 2009.
Shriver was born Nov. 9, 1915, in Westminster, Md., into a socially prominent family.
After receiving his law degree at Yale and serving in the Navy during World War II, Shriver took a position as assistant manager of the massive Chicago Merchandise Mart, which was controlled by Joseph P. Kennedy, the patriarch of the Massachusetts clan that produced a president and two senators. Shriver turned the Chicago property into a moneymaker and also got involved in public service, becoming chairman of the Chicago school board.
His good bearing and fine personal appearance made him a logical political aide to his brother-in-law, Sen. John F. Kennedy, in his successful quest for the Democratic presidential nomination in 1960.
Following the election, Kennedy rewarded Shriver for his services by naming him first director of the newly created Peace Corps in 1961. Three years later and slightly more than two months after the assassination of President Kennedy, President Johnson named Shriver director of the Office of Economic Opportunity. In 1968, in the twilight of the Johnson administration, Shriver was named ambassador to France and remained in that post for a year during the Nixon administration.
In March 1970 Shriver left the diplomatic world to return to private law practice in Washington and New York until 1972 when he was summoned to replace Eagleton.
Shriver was an effective campaigner, but the Nixon ticket was more powerful and won by a landslide.
When Shriver decided to enter the primaries in 1976 rival politicians described him as a "stalking horse" for his brother-in-law, Sen. Edward M. Kennedy, D-Mass., who was not a candidate. Shriver denied he was being used and continued to campaign until the state primaries revealed he would not be able to win the nomination.