Keeshan was an adopted member of the Dartmouth College class of 1942, receiving an honorary doctorate from the college in 1975. He was also awarded an honorary Doctor of humane letters by Fordham University in 1975. Le Moyne College, a Jesuit liberal arts college in Syracuse, New York, awarded him an honorary Doctor of humane letters in 1983. He was awarded an honorary doctorate by the College of New Rochelle in 1985, after serving for several years on its board of trustees. In 1997, he received an honorary doctorate from Middlebury College, the alma mater of his grandson Britton Keeshan, for his work in children's literacy.

Keeshan was born in Lynbrook, New York. After an early graduation from Forest Hills High School in Queens, New York, in 1945, during World War II, he enlisted in the United States Marine Corps Reserve, but was still in the United States when Japan surrendered. He attended Fordham University on the GI Bill and a few years at Hillsdale College.

Network television programs began shortly after the end of the war. Howdy Doody, an early show which premiered in 1947 on NBC, was one of the first. Debuting on January 3, 1948, Keeshan played Clarabell the Clown, a silent Auguste clown who communicated by honking several horns attached to a belt around his waist. One horn meant "yes"; two meant "no". Clarabell often sprayed Buffalo Bob Smith with a seltzer bottle and played practical jokes. Keeshan gave up the role in 1952, and was replaced.

By September 21, 1953, Keeshan was back on the air on WABC-TV (New York City), in a new children’s show, Time for Fun. He played Corny the Clown, and this time he spoke. Later that same year, in addition to Time for Fun, Keeshan began Tinker's Workshop, a program aimed at preschoolers, with him playing the grandfather-like Tinker.

Developing ideas from Tinker's Workshop, Keeshan and his long-time friend Jack Miller submitted the concept of Captain Kangaroo to the CBS network, which was looking for innovative approaches to children's television programming. CBS approved the show, and Keeshan starred as the title character when it premiered on CBS on October 3, 1955. Keeshan described his character as based on "the warm relationship between grandparents and children." The show was an immediate success, and he served as its host for nearly three decades.

Keeshan also had a Saturday morning show called Mister Mayor during the 1964–65 season. Keeshan, in his role as the central character in both Captain Kangaroo and Mister Mayor, heavily promoted the products of the Schwinn Bicycle Co., a sponsor, directly on-air to his audience. By 1972, Keeshan had introduced another character on Captain Kangaroo to recommend Schwinn products, Mr. Schwinn Dealer, due to the Federal Trade Commission ruling against children's show hosts directly endorsing their sponsor's products during their programs after 1969.

Keeshan had a longtime close friendship with Fred Rogers of Mister Rogers' Neighborhood. Both paid visit to each other's shows (Keeshan on Mister Rogers' Neighborhood and Rogers on Captain Kangaroo) in 1970, and two appeared together on the PBS TV special Springtime with Mister Rogers in 1980. The following year, Fred Rogers appeared briefly in Keeshan's TV special Good Evening, Captain (following Keeshan's 1981 heart attack), in which Rogers and Dick Clark both presented Keeshan with flowers at the end of the show.

Keeshan suffered a severe heart attack just moments after stepping off a plane at Toronto International Airport on July 13, 1981, which pushed the start of a revamped version of his show back to at least mid-August. He had come to the city to accept a children's Service award.

Following the heart attack, Keeshan received three Emmy awards for Outstanding Performer in 1982, 1983, and 1984. Despite these accolades, Keeshan's show was shortened from its hour-long format to a half hour in 1981, to make room for the expansion of the CBS Morning News lineup. The program was retitled Wake Up with the Captain, and was moved to a new 7:00 am time slot. At the start of 1982, the show was rescheduled to an even earlier slot of 6:30 am. In the fall of 1982, CBS installed it as a weekend-only hour offering, and two years later, in the fall of 1984, the show became a Saturday half-hour entry.

Tired of CBS's constant reductions of his show, Keeshan left Captain Kangaroo when his contract with the network ended in December 1984, just nine months shy of the show's 30th anniversary. By 1987, repeats of the show were airing daily on many PBS stations.

After Captain Kangaroo ended, Keeshan hosted 1985's CBS Storybreak, which featured animated versions of children's literature. Keeshan appeared in framing sequences for the animated stories, showcasing the book versions and suggesting similar books for the viewers to seek out. In 1987, Keeshan founded Corporate Family Solutions with former Tennessee Republican Governor Lamar Alexander. The company provided day-care programs to businesses.

In the 1990s, Keeshan expressed an interest in bringing back a new version of Captain Kangaroo as a gentler and kinder answer to the violent cartoons on children's television. Despite having sponsors and television stations lined up, Keeshan was unable to obtain permission from ICM, the company that owned the rights to Captain Kangaroo at that time.

Keeshan lived on Melbury Road in Babylon Village, Long Island, New York, before moving to spend the last 14 years of his life in Norwich, Vermont, where he became a children's advocate, as well as an author. His memoirs, entitled Good Morning, Captain, were published in 1995 by Fairview Press. He was a strong advocate against video game violence and took part in congressional hearings in 1993. In addition, he joined with parents' groups in the 1980s who protested children's TV shows based on then present toys on the market, like He-Man and Transformers; he felt that toys turned into TV shows did not teach children anything about the real world. He also made a rare film appearance in The Stupids in 1996.

Keeshan died in Windsor, Vermont, on January 23, 2004, at age 76. He was survived by three children: Michael Derek, Laurie Margaret, and Maeve Jeanne. His wife of 45 years, Anne Jeanne Laurie Keeshan, died February 25, 1996. Keeshan's grandson, Britton Keeshan, became the youngest person at that time to have climbed the Seven Summits by climbing Mount Everest in May 2004. He carried photographs of his grandfather on that ascent, and buried a photo of the two of them at the summit.

An urban legend claims that actor Lee Marvin said on The Tonight Show that he had fought alongside Keeshan at the Battle of Iwo Jima in February–March, 1945. However, Marvin not only never said this, but had not served on Iwo Jima (having been hospitalized from June 1944 until October 1945, from wounds received in the Battle of Saipan), and Keeshan himself never saw combat, having enlisted too late to serve overseas.