The actor, who played a recurring character on the hit sit-com Cheers passed away in North Carolina on Monday night.
His son, Dashiell Anderson, told TMZ his dad died of natural causes.
Harry's found fame in the US playing Judge Harry T. Stone in the sit-com Night Court, which ran between 1984 to 1992.
On three occasions he was nominated for an Emmy for Outstanding Lead Actor in a Comedy Series.
He had a recurring guest role as con man Harry "The Hat" Gittes on Cheers.
As well as comedy, he also appeared as and adult Richie Tozier in a 1990 TV adaptation of Stephen King's It.
Anderson was also a talented magician and toured his act exhaustively, having fell in love with the art form watching hustlers in restaurants in his home town of Newport, Rhode Island.
He made eight appearance on Saturday Night Live between 1981 and 1985.
In the 1990s, he and second wife, Elizabeth, opened a small shop in New Orleans called Sideshow, selling magic tricks and curiosities.
His other TV credits include The New Adventures of Superman, Comedy Bang! Bang!, 30 Rock and Tales From the Crypt.
As a resident of New Orleans, he featured on film documentary Hexing a Hurricane, charting the area after it was hit by Hurricane Katrina.
In 2006 he moved to Asheville, North Carolina.
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