Vee died on Monday following a five-year battle with Alzheimer's disease, reported BBC.
His son Jeff Velline said the singer died peacefully surrounded by family.
It was "the end of a long hard road", Mr Velline said. He described his father as "a person who brought joy all over the world", adding: "That was his job."
Born on April 30, 1943 in Fargo, North Dakota, United States, Vee became popular in 1959 at the age of 15 when he replaced Buddy Holly after the singer's death in a plane crash.
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The singer's first hit in the Billboard charts was "Devil or Angel."
A series of hits followed, including "The Night Has a Thousand Eyes," "Come Back When You Grow Up," "Please Don't Ask about Barbara" and "Punish Her."
Vee last performed at his own retirement show in 2011, not long after he was diagnosed with Alzheimer.
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