Gleason was born in New York City and graduated from Columbia University (where he was news editor of the Columbia Daily Spectator) in 1938. During World War II, he worked for the Office of War Information.
In 1947, he moved to San Francisco and began contributing to the San Francisco Chronicle in 1950, initiating the first regular coverage of jazz and pop music in the mainstream US media. Gleason was the first critic to review folk, pop, and jazz concerts with the same attention and space as was given to classical music. He interviewed such luminaries as Frank Sinatra, Hank Williams, Elvis Presley, and Fats Domino. Gleason was one of the first critics to perceive the importance of Lenny Bruce, Bob Dylan, and Miles Davis. He wrote liner notes for a broad variety of releases, including the 1959 Sinatra album No One Cares and the 1970 Davis album Bitches Brew. From 1948 to 1960, he doubled as an associate editor and critic for Down Beat. He also taught music appreciation courses at University of California Extension (1960-1963) and Sonoma State University (1965-1967).
Gleason was both an observer and a contributor to what is sometimes termed the San Francisco Renaissance, the era of increased cultural vitality in that city which began in the mid-1950s and fully bloomed in the mid-to-late 1960s. In the later 1960s, Gleason was a widely respected commentator and he chose to write supportively of the better cut of the Bay Area rock bands, such as Jefferson Airplane and the Grateful Dead. However, Gleason was sometimes criticized for minimizing the importance of or simply ignoring acts from Los Angeles. But others judged that he was making a valid distinction between works of creative vitality and music business product. In any case, Gleason was a key contributor to the growth and range of San Francisco region's vibrant music scene of the 1960s and after.
Gleason was a contributing editor to Ramparts, a prominent leftist magazine based in San Francisco, but quit after editor Warren Hinckle criticized the city's growing hippie population. With Jann Wenner, another Ramparts staffer, Gleason founded the bi-weekly music magazine, Rolling Stone, to which he contributed as a consulting editor until his death in 1975. He was in the midst of an acrimonious split with Wenner and the magazine when he died. For ten years he also wrote a syndicated weekly column on jazz and pop music that ran in the New York Post and many other papers throughout the United States and Europe.
Gleason's articles also appeared other publications, including The New York Times, The Guardian, The Times, New Statesman, Evergreen Review, The American Scholar, Saturday Review, the New York Herald Tribune, the Los Angeles Times, the Chicago Sun-Times, the Sydney Morning Herald, Playboy, Esquire, Variety, The Milwaukee Journal1 and Hi-Fi/Stereo Review.