Keane was born in Philadelphia, Pennsylvania, the son of cartoonist Bil Keane, creator of the The Family Circus, and Thelma "Thel" Carne Keane. He was raised in Paradise Valley, Arizona.

Keane's interest in art developed as a child by observing his father's work as a cartoonist. (Glen's younger self is represented in his father's comic strip as the character of "Billy"). In his early attempts to draw, his dad gave him a copy of Burne Hogarth's Dynamic Anatomy, and instructed him to analyze the body forms and the creative approach to life drawing. After high school, Glen applied to the California Institute of the Arts-School of Art, opting out of accepting a football scholarship from another college. In a lucky twist of fate, his application was accidentally sent to the Program in Experimental Animation (then called Film Graphics), where he was mentored under the now-renowned animation teacher Jules Engel.

Keane left CalArts in 1974 and joined Disney the same year. His debut work, which was created over a 3-year period, was featured in The Rescuers, for which he was an animator for the characters of Bernard and Penny, alongside the famed Ollie Johnston. In 1975, during the production of his debut film, Keane married Linda Hesselroth, and they are the parents of design artist Claire Keane, and computer graphics artist Max Keane.

After "The Rescuers" was completed, Keane went on to animate Elliott the Dragon in Pete's Dragon. Keane also animated the climactic bear showdown in The Fox and the Hound. In 1982, after being inspired by the groundbreaking film Tron, he worked with director John Lasseter (Toy Story, Toy Story 2) on a 30-second test for Where the Wild Things Are (that was greenlit by Tom Willhite). The test integrated traditional character animation and computer-generated backgrounds (see YouTube), and, like Tron, was a cooperation with MAGI. It was also Disney's first experimentation with digital inked and painted characters. But, the project turned out to be too expensive, and the studio was unwilling to invest further in the planned featurette. The test for Where the Wild Things Are was revolutionary for its time, and a predecessor to the famous ballroom scene in Beauty and the Beast.

In 1983, Keane left Disney as a contracted employee and worked as a freelance artist. During this time he worked on the character of Professor Ratigan in Disney's The Great Mouse Detective. He also did some work on The Chipmunk Adventure where he did the sequences of "Boys and Girls of Rock N' Roll" and "Getting Lucky". He returned to Disney to work on the characters of Fagin, Sykes and Georgette for Oliver & Company. Keane rose to lead character animator, becoming one of the group sometimes referred to as the "Nine New Men". In this post he was responsible for animating some of Disney's most memorable characters in what has been referred to as the "New "Golden Age" of Disney Animation. Keane designed and animated the character of Ariel in the 1989 film The Little Mermaid. Then the eagle Marahute in The Rescuers Down Under. Subsequently, Keane worked as the supervising animator on the title characters for three Disney hit features: Aladdin, Beauty and the Beast and Pocahontas.

While living with his family in Paris, France for three years, Keane completed work on Disney's 1999 Tarzan for which he drew the eponymous character. Keane then returned to Disney's Burbank studio as the lead animator for Long John Silver in Treasure Planet. In 2003, Keane began work as the director of Disney's CGI animated film, Tangled (based on the Brothers Grimm story Rapunzel), slated for release in 2010. In Tangled, Glen and his team hoped to bring the unique style and warmth of traditional cel animation to computer animation. In October 2008, due to some "non-life threatening health issues", Keane stepped back as director of Tangled, but remained the film's executive producer and an animating director.

In addition to his work as an animator, Keane is the author and illustrator of a series of children's Bible parable books featuring Adam Raccoon and King Aren the Lion.