Gifford, who was married to talk show host Kathie Lee Gifford, was 84.
"It is with the deepest sadness that we announce the sudden passing of our beloved husband, father and friend, Frank Gifford," the Gifford family said in a statement.
"We rejoice in the extraordinary life he was privileged to live, and we feel grateful and blessed to have been loved by such an amazing human being. We ask that our privacy be respected at this difficult time and we thank you for your prayers."
Gifford was face of the New York Giants franchise during its glory years of the 1950s and 1960s, bringing the team to five Eastern Conference titles and one NFL championship.
"Frank Gifford was the ultimate Giant. He was the face of our franchise for so many years. More importantly, he was a treasured member of our family," said Giants President John Mara, whose father, former Giants owner Wellington Mara, was Gifford's presenter at his 1976 induction into the Pro Football Hall of Fame.
"For my siblings and me, Frank was like a revered older brother whom we looked up to and admired. We loved him and will miss him terribly."
By the time Gifford joined the New York Giants as their No. 1 draft pick in 1952, he already had established his gridiron bona fides in high school and college -- despite his father's wishes.
Gifford was born in Santa Monica, California, in 1930, the youngest of Weldon and Lola Mae Gifford's three children. Gifford was a Depression-era child although he has said he didn't realize it at the time. Weldon Gifford was an oil worker, and the family traveled the country for his job before settling in Bakersfield, where Gifford attended high school.
"I had a great mother and father. My dad was out of work more than he was in work," Gifford told CNN's Larry King in 1993. "But I mean, we didn't know that... They somehow or other kept this family together."
Gifford excelled in sports because he was "competing with an older brother all the time," his only constant friend during his itinerant childhood.
"My dad tried to get me to quit playing football in high school. I hurt my ankle and, of course, everyone in my family had always gone right into the oil fields, and there was a concern that I was really going to be hurt, on his part," he told King.
After completing high school in 1948, Gifford spent a year at Bakersfield Junior College earning academic credits for the University of Southern California in Los Angeles, where he was offered a football scholarship.
At the University of Southern California, Gifford played offense and defense and won All-American honors as a senior before he was drafted into the NFL.
As the NFL's Most Valuable Player in 1956 he brought the Giants to a league championship. When a head injury from a game against the Philadelphia Eagles put him on the sidelines in 1961, many believed his reign had ended. He returned in 1962 and switched from halfback to flanker to take advantage of his great pass-catching skills, regaining his star status once again, according to his Pro Football Hall of Fame profile
He was selected to eight Pro Bowls, playing defensive back, halfback and flanker, before retiring from professional football in 1964. But his career in sports was far from over.
Gifford was one of the first American sports stars to shift into television sportscasting. He became part of ABC's "Monday Night Football" lineup in 1971, joining fellow NFL veteran Don Meredith and broadcaster Howard Cosell.
He was inducted into the College Football Hall of Fame in 1976 and the Pro Football Hall of Fame in 1977.
For much of his career, his personal life was a secondary subplot, until he married Kathie Lee Epstein Johnson in 1986, who was 23 years his junior. He had three children with his first wife, Maxine Ewart, whom he married in 1952. The couple divorced and in 1978 Gifford married a second time to Astrid Narss.
His marriage to Narss has just ended in 1986 when he met his soon-to-be third wife. He was filling in for David Hartman on "Good Morning America" when the two crossed paths around 5:30 in the morning while he was getting ready.
"I was putting my contact lenses in, and I'm bending over at the thing, and I had nothing but my shorts on, and she made some comment...about something about, 'I've seen a lot of tight ends...' but just kept right on walking down the hall," Gifford told King in 1993.
"And I asked who that was, and it was Kathie Lee Johnson. And I'd seen her on television, and I could not believe how unbelievably up she was. But that's her."
The couple had two children and Kathie Lee Gifford often described her marriage in glowing terms in the press.
"Frank is my husband, my confidant, lover, therapist, parenting partner and best friend. We depend on each other for security, for emotional, sexual and spiritual fulfillment, and for companionship," Kathie Lee Gifford wrote in her 1992 memoir, "I Can't Believe I Said That!"
The rosy picture was shattered in 1997 by news that Gifford was having an affair. Kathie Lee Gifford went on a media offensive and declared that their marriage would last. Gifford reduced his role on "Monday Night Football" and retired from network broadcasting in 1998.
Their marriage endured to the end. Kathie Lee Gifford was one of many to publicly mourn Gifford's death Sunday with a message on Twitter
"Deeply grateful to all for your outpouring of grace. We are steadfast in our faith & finding comfort in knowing where Frank is."