Clark, known for hosting shows such as American Bandstand and New Year's Rockin' Eve, passed away after a "massive heart attack" yesterday.
Disney, which owns American Bandstand's network ABC, has now released a statement explaining that it was "proud" to work with Clark.
The Walt Disney Company's chairman and CEO Robert A Iger said: "For more than half a century, Dick Clark brought the best of American music to audiences across the country, creating careers and countless fans for artists on his iconic shows American Bandstand and New Year's Rockin' Eve.
"We're proud that ABC was home to those programmes and will always be part of his legacy. On behalf of everyone at Disney and ABC, we send our sincere condolences to Dick's family, as well as the three generations of fans who will miss him as much as we do."
Ryan Seacrest, who co-hosted New Year's Rockin' Eve, paid tribute to Clark on last night's American Idol, saying: "He will be missed greatly."
President Barack Obama has also offered his condolences, saying: "As we say a final "so long" to Dick Clark, America's oldest teenager, our thoughts and prayers are with his family and friends - which number far more than he knew."
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Watch a 1999 interview with Dick Clark below:
Picture gallery - Dick Clark: Career in pictures