President Barack Obama led the tributes to the entertainer, hailing his "groundbreaking achievements" which "reshaped (America's) television landscape forever."
Clark, famous for shows including "American Bandstand" and "Dick Clark's New Year's Rockin' Eve" suffered a cardiac arrest after being admitted to hospital in Santa Monica, California, on Tuesday.
"Entertainment icon Dick Clark passed away this morning at the age of 82 following a massive heart attack," said the family statement, released by his publicist Paul Shefrin.
Clark "entered St. John's Hospital in Santa Monica last night for an outpatient procedure. Attempts to resuscitate were unsuccessful," it added.
The entertainer, whose Dick Clark Productions remains a key force in the industry, was known to generations of US television viewers as "America's oldest teenager."
Clark suffered a stroke in 2004 which forced him into retirement, although he continued to appear on the New Year's Eve special alongside celebrity host Ryan Seacrest.
Seacrest, the host of "American Idol," was among the first to pay tribute to Clark.
"I am deeply saddened by the loss of my dear friend Dick Clark. He has truly been one of the greatest influences in my life," he said on his Twitter account.
In Washington, the White House issued a statement from Obama, saying that with "American Bandstand," Clark "introduced decades' worth of viewers to the music of our times.
"He reshaped the television landscape forever as a creative and innovative producer. And, of course, for 40 years, we welcomed him into our homes to ring in the New Year.
"But more important than his groundbreaking achievements was the way he made us feel -- as young and vibrant and optimistic as he was."
In Los Angeles, a wreath was placed on Clark's sidewalk star on the Hollywood Walk of Fame.
Verdine White, bassist for the band Earth, Wind and Fire who played on "American Bandstand," said: "He was a wonderful guy to work for... he gave you everything you needed so you could be the best you could be.
"Dick was like another member of the band," he told CNN, adding that Clark was among the first to put African American musicians on national US television. "His legacy to rock and roll is unparalleled," he said.
Clark's physical youthfulness was also astonishing. "He was ageless. He looked the same for 50 years," said White.
A New York native, Clark began his career at 17 and worked his way up to television and radio anchor both there and in Philadelphia -- where he became host of its "Bandstand" show in 1956.
He created Dick Clark Productions a year later, taking the show nationwide as "American Bandstand." The company still produces shows including the Golden Globes, the American Music Awards and the Academy of Country Music Awards.
Clark reflected on his career in 2006, when he was honored at the Emmy Awards show in Los Angeles.
"Before I had my stroke, I was thinking about all of the things I have become involved in over my life -- music, comedy, drama, game and talk shows, even reality TV," he told the audience.
"I now realize that I have accomplished my job and dream, to be in show business. Everybody should be so lucky to have their dreams come true," he added.
Clark is survived by his wife, Kari Wigton, and has three children from previous marriages.