Morse's son Charlie confirmed his father's death to Eyewitness News Wednesday night.
Morse starred in the 1961 Broadway production of "How to Succeed in Business Without Really Trying" and won a Tony Award for his performance. In 1967, he starred in the film version.
He also appeared in the AMC series "Mad Men." His performance as Bertram Cooper on the show earned him five Emmy nominations.
In 1992, he won his second Tony Award. It was for playing Truman Capote in "Tru."
At the age of 85, he returned to Broadway to star with Nathan Lane in the 2016 revival of "The Front Page."
Further details about Morse's death were not immediately available.