Osborne was born on May 3, 1932, in the small town of Colfax, Washington, where he was raised. His parents were Robert Eugene Osborne, a public school Teacher, and Hazel Ida (née Jolin). Osborne graduated from the University of Washington School of Journalism in 1954.

One of Osborne's early television appearances was in a 1959 episode of Westinghouse Desilu Playhouse called "Chain of Command", starring Hugh O'Brian. He was also featured in the Christmas Day Desilu Playhouse installment "The Desilu Revue" in December 1959. He also had small roles in such TV shows as The Californians and the 1962 pilot episode of The Beverly Hillbillies, "The Clampetts Strike Oil" (in the role of Jeff Taylor). He refrained from signing on for the series, however, thinking the show would not be a success, and instead focused his attention on acting in television commercials.

Ball suggested that Osborne focus his energies on becoming a Journalist, as he would often quip, "especially after she saw me act". After The Beverly Hillbillies, Osborne would focus more on writing and journalism. In 1965, Osborne had his first book published, Academy Awards Illustrated.

In 1977, Osborne began his long-standing stint as a columnist for The Hollywood Reporter. The following year, he published 50 Golden Years of Oscar, which won the 1979 National Film Book award. Having joined the Los Angeles Film Critics Association, he was elected its President in 1981, and served as such till 1983. In 1982, Osborne began a five-year stint as the entertainment reporter on KTTV Channel 11 in Los Angeles. In addition, he began his Rambling Reporter column for The Hollywood Reporter, published five times weekly.

Osborne had moved to New York City in the late 1980s. During his lifetime, few details of his personal life were reported, but upon his death it was confirmed that he had been in a 20-year relationship with David Staller of Gingold Theatrical Group; it was Staller who confirmed Osborne's death to the media.

Osborne won the Publicists Guild of America 1984 Press Award. He also received an honorary doctorate from the Academy of Art University in 2005, and was awarded a star at Vine Street on the Hollywood Walk of Fame in 2006. In 2007, he received the National Board of Review's william K. Everson Award.

In 1994, Ted Turner created Turner Classic Movies as a competitor to American Movie Classics (now known as AMC). Osborne was selected as the host of their nightly broadcasts. For TCM, in addition to hosting four primetime movies seven days a week, he was also the host of special one-on-one "Private Screening" interviews featuring many familiar actors and Directors. Beginning in 2006, Osborne also co-hosted TCM's The Essentials. His co-hosts were Molly Haskell from 2006 to 2007, Carrie Fisher from 2007 to 2008, Rose McGowan from 2008 to 2009, Alec Baldwin from 2009 to 2011, Drew Barrymore and finally Sally Field.

Osborne also participated in events at the Paley Center for Media in New York City saluting the television careers of Lucille Ball and Cloris Leachman. Beginning in 2005, Osborne hosted the annual "Robert Osborne's Classic Film Festival" in Athens, Georgia. The non-profit event is held by the University of Georgia’s Grady College of Journalism and Mass Communication. In 2010, Osborne hosted the very first TCM Classic Film Festival, and participated in subsequent annual festivals.

In 2011, Osborne became ill and TCM announced that Osborne would be taking "a short break from his TCM hosting duties for minor surgery, followed by a vacation." Osborne continued to appear on Saturday nights, hosting "The Essentials" with Alec Baldwin. In 2012, Osborne began to share some of his hosting duties with Ben Mankiewicz. Mankiewicz hosted primetime films two nights a week as well as many daytime events. Osborne stated that he would continue to work “as long as I have health, and as long as I think I look O.K. on camera.” He also said, “If I really couldn’t do it with enthusiasm, that would be the time to quit.”

In 2014, as part of an exclusive programming deal with Disney, TCM agreed to become the sponsor of The Great Movie Ride. The attraction underwent a refurbishment in 2015, with the addition of a new pre-show and post-show hosted by Osborne, who also provides onboard narration to the ride. The changes were unveiled on May 29, 2015.

In January, 2016, Osborne was given the inaugural william Cameron Menzies Award from the Art Directors Guild, recognizing his 35 years as a film Historian, columnist and critic championing visual entertainment.

Osborne retired from the air in early 2016 due to ill-health and missed a number of TCM annual events over the next year. Osborne died at his New York City apartment in the Osborne on West 57th Street on Monday, March 6, 2017, from natural causes. He was 84.

In March 2018, Turner Classic Movies announced the establishment of the Robert Osborne Award, to be presented at the annual TCM Classic Film Festival "to an individual whose work has helped keep the cultural heritage of classic films alive and thriving for generations to come." The inaugural recipient was film Director Martin Scorsese for his work with The Film Foundation, which Scorsese helped found in 1990.