Rankin was 89 years old and died in his Harrington Sound home following an illness, the Royal Gazette, Bermuda, reported.
"A great man of innate curiosity who gave so willingly of his time -- I was blessed to be in his circle of friends," Masterworks Foundation head Tom Butterfield said.
Rankin and his partner Jules Bass founded Rankin/Bass Productions in the 1960s and created "Frosty the Snowman," "Santa Claus is Coming to Town" and "A Year Without a Santa Claus."
He also wrote, produced or directed more than a dozen feature films.
"It's hard to be good at anything," Rankin said in 1996. "If you're passionate, the chances are that you will find a job that will make you happy."
Rankin was born in New York City and was the son of actors Arthur Rankin and Marian Manfield, the Hollywood Reporter said.
His grandfather, Harry Davenport, played Dr. Meade in "Gone With the Wind."
He began his career as an art director at ABC in the late 1940s.
Rankin is survived by his wife, Olga, and his two sons, Todd and Gardner.