Windom was born on September 28, 1923, in New York City. He was the son of Isobel Wells (née Peckham) and Paul Windom, an architect. He was the great-grandson of the United States Secretary of the Treasury of the same name. He served in the United States Army in the European Theater of Operations in World War II, as a paratrooper with Company B, 1st Battalion 508th Parachute Infantry Regiment, 82nd Airborne Division.  Windom’s first motion picture role was as Mr. Gilmer, the prosecutor of Tom Robinson in the 1962 Academy Award-winning To Kill a Mockingbird. In 1968, he starred with Frank Sinatra in The Detective, playing a homophobic killer. The role received great reviews from The New York Times.

From September 1963 to April 1966, he co-starred in the television version of the previous film, The Farmer’s Daughter, a series about a young Minnesota woman who becomes the housekeeper for a widowed congressman. In the 1969–1970 NBC series My World and Welcome to It, Windom played the James Thurberesque lead and received an Emmy Award for Outstanding Continued Performance by an Actor in a Leading Role in a Comedy Series. After the cancellation of the series, Windom toured the country for a time in a one-man Thurber show. After the run was completed Windom filmed the pilot for a new series Is there a Doctor in the House? with Rosemary Forsyth. The pilot was written with both actors in mind for the two starring roles, and while it was well received by the critics and in viewership ratings in both its first run and a rerun in the summer of 1971, it was not picked up for a series.

He was a regular for a decade on the series Murder, She Wrote with Angela Lansbury as a mystery writer. His initial appearance in the role was in October 1985. (He had previously appeared as a guest star playing another character in April 1985.) The producers enjoyed his work, and consequently invited him to return at the beginning of the second season to take on the role permanently. He briefly left the show to work on another series in 1990, but the show was short-lived and he returned to Murder, She Wrote as a semi-regular for the remainder of the run of that series.  To fans of science fiction television, Windom was best known as the tortured Commodore of the USS Constellation Matt Decker in the Star Trek episode “The Doomsday Machine”, a role he reprised nearly 40 years later for Star Trek New Voyages.

According to his widow, Patricia Tunder Windom, the actor died on August 16, 2012, at the age of eighty-eight at his home in Woodacre, California, from congestive heart failure. He was survived by four of his children – Rachel, Heather, Hope and Rebel – and four grandchildren.