Mr Shriver, shown with wife Eunice Kennedy, ran President Lyndon Johnson’s anti-poverty programme Sargent Shriver, the first US Peace Corps director, Democratic vice-presidential candidate and brother-in-law to President John F Kennedy, has died.
His son, Anthony Kennedy Shriver, said he had died on Tuesday aged 95 after two days in hospital.
Mr Shriver, who was George McGovern’s vice-presidential running mate in 1972, married Eunice Kennedy in 1958.
His son-in-law is former California Governor Arnold Schwarzenegger.
Mr Shriver also ran President Lyndon Johnson’s “War on Poverty” programme.
US President Barack Obama praised Mr Shriver as “one of the brightest lights of the greatest generation”, and said he “came to embody the idea of public service”.
“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,” Mr Obama said in a statement.
“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.”
Current Peace Corps director Aaron Williams said the whole Peace Corps community was “deeply saddened” by Mr Shriver’s death.
“Shriver was a distinguished public servant and a visionary leader who accomplished much in his life of public service, but to those of us in the Peace Corps family, he served as our founder, friend, and guiding light for the past 50 years,” he said in a statement.
Mr Shriver’s death comes less than 18 months after that of his wife, who died in August 2009 aged 88.
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