The former teen idol enjoyed more than 30 hit records in his heyday and had his own TV show.
His daughter, Tricia Leigh Fisher, told reporters Fisher died on Wednesday night at his home in Berkeley, California, of complications from hip surgery.
His marriage to actress and singer Debbie Reynolds produced two children, including Carrie Fisher, who played Princess Leia in the original Star Wars trilogy.
When his best friend, the producer Mike Todd, was killed in a 1958 plane crash, Fisher comforted his widow Elizabeth Taylor.
Sensational headlines followed when he divorced Reynolds and married Taylor in 1959.
The marriage lasted five years and Taylor went on to marry Richard Burton.
Fisher sold millions of records with songs including Thinking of You, I'm Yours, Wish You Were Here and Count Your Blessings.
In 1983, he attempted a comeback but the tour was unsuccessful.
Fisher, who was born in Philadelphia, was married five times in total and his other wives included Connie Stevens.
Fisher's family said in a statement: "Late last evening the world lost a true America icon.
"One of the greatest voices of the century passed away."