Eagleton, 77, had suffered from a variety of illnesses and ailments in recent years. A cause of death was not disclosed. McCaskill spokeswoman Adrianne Marsh said the family was expected to release a statement later Sunday.
Eagleton was born in St. Louis in 1929, the son of noted civil trial attorney Mark Eagleton, who once ran unsuccessfully for mayor and encouraged his son's interest in politics. He was elected circuit attorney at age 26 in 1956, just three years after graduating from Harvard Law School. He was the youngest man ever elected to the position.
He was elected Missouri attorney general in 1960 and lieutenant governor in 1964 before winning election to the U.S. Senate in 1968. He won re-election in 1974 and 1980, retiring after his third term.
After McGovern chose the 42-year-old senator as his running mate, it was soon learned that Eagleton had suffered from depression and twice undergone shock treatments a decade earlier.