Klugman's sons Adam and David confirmed that the Emmy award-winning actor passed away on Christmas Eve afternoon. His wife Peggy was at his bedside, reported Ace Showbiz.
"He had a great life and he enjoyed every moment of it, and he would encourage others to do the same," Adam said.
"His sons loved him very much. We'll carry on in his spirit," added David.
Born Jacob Joachim Klugman on April 27, 1922 in Philadelphia, he enjoyed a long career, taking up acting following his discharge from the US Army at the end of the Second World War.
In addition to his portrayal of tenacious and principled medical pathologist Dr Quincy, Klugman is probably best known for playing laid-back sports reporter Oscar Madison in 'The Odd Couple' on Broadway, and in the subsequent 1970s ABC sitcom of the same name.
Klugman also appeared in shows such as 'The Twilight Zone', 'Diagnosis Murder', 'The Defender' and 'The Fugitive'.
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He was a Tony Award nominee, a triple Emmy winner and ten-time nominee, and received a Golden Globe in 1974 for his work on The Odd Couple.
He lost a vocal chord as a result of throat cancer in the 1980s, but taught himself to speak again and returned to acting in a Broadway revival of Three Men on a Horse in 1993.
Klugman is survived by his wife, his two sons from his first marriage to Brett Somers, and two grandchildren.