Claxton died Saturday at Cedars Sinai Medical Center in Los Angeles of complications stemming from congestive heart failure, his son Christopher said.
He was best known for his soulful portraits of jazz artists such as Chet Baker, and he went on to photograph Dylan and other musicians such as Joni Mitchell and Tom Jones. His images graced the covers of numerous albums.
Claxton, a founding member of The Recording Academy, started his photography career in 1952 while a student at University of California, Los Angeles.
He also worked with Sinatra, Steve McQueen and Rebecca De Mornay, and his photographs regularly appeared in such magazines as Life, Paris Match and Vogue.
In the 1960s, Claxton collaborated with his wife, fashion model, to create a collection of iconic images featuring Rudi Gernreich's fashion designs.
A film he directed from that era, "Basic Black," is considered by many to be the first "fashion video" and is now part of the collection of the Museum of Modern Art in New York.
Claxton also wrote 13 books and held dozens of exhibitions of his work around the world.
In 2003, he won the Lucie award for music photography at the International Photography Awards.
"He was a great photographer and a wonderful man who touched the lives of his friends through his generosity, charm and kindness," said his publisher Benedikt Taschen, founder and owner of Taschen Publishing, in a statement. "Bill was very close to my heart and a pillar of our publishing house."