Goldman was born in Oakland, California and raised in Watsonville, California. As a youth, Goldman was active in Sports, an infielder in baseball and quarterback in high school football, he studied piano and enjoyed model-making and drawing. Before devoting himself entirely to the arts, he served as an electronics technician in the United States Air Force from 1962 to 1967, assigned duties in Japan and Germany. He received his Associate of Arts Degree in 1969 from Cabrillo College, and he graduated in December 1971 with a Bachelor of Fine Arts degree in Life Drawing and Art History from the University of Hawaii.

While in college he married elementary Teacher Janith Eileen Brand in April 1968. They separated in 1983 and divorced in 1987. They have two children, Kip and Andrew. In 2001 Goldman & Bluth received Lifetime Achievement Awards for their dedication and contribution to the art of animation from Animation Magazine, and in 2005, at the Savannah Film Festival, Lifetime Achievement Awards for animation, from the Savannah College of Art & Design, to which they gave their animation art archive. Goldman remarried in late 1988 to film cutter Cathy (Bassett) Carr. She and her three children John Carr, Jason Carr and Joanna Carr moved with him to Dublin, Ireland in 1986. Together they have nine grandchildren.

Goldman began his career in animation when he joined Walt Disney Productions in February 1972. His first assignment was as an in-betweener to legendary Disney Animator Frank Thomas on the film Robin Hood. He then worked alongside Don Bluth, as an Animator, on Winnie the Pooh and Tigger Too! and The Rescuers before serving as Directing Animator on Pete's Dragon and The Small One.

Goldman has been a member of the Academy of Motion Picture Arts and Sciences since 1978.

Divided by disagreements over story and production values, Goldman, along with Bluth and Pomeroy, resigned from Walt Disney Productions to establish their independent animation studio, Don Bluth Productions, in 1979. The departure was highly publicized and the trio was dubbed "Disney Defectors" by news reporters.

Since leaving Disney, the team produced several feature films, starting with The Secret of NIMH, which won the Saturn Award for "Best Animated Feature" from the Science Fiction, Fantasy and Horror Film Academy. In late 1982, Composer Jerry Goldsmith introduced them to Director Steven Spielberg. Their first collaboration with Spielberg, which began production in January 1985, An American Tail, was released in November 1986 and ushered in a new era of success for the full-length animated feature, becoming the highest-grossing animated film up to that time.

Goldman was a Producer on the highly successful animated laser disc interactive video games Dragon's Lair, Space Ace and Dragon's Lair II: Time Warp. Dragon's Lair received the Inkpot Award for the "First Interactive Laser Disc Arcade Game" and an Arkie Award for the "Best Arcade Audio/Visuals". Financial difficulties with their distributor cut them off from financing and forced them to seek protection from bankruptcy in 1984. It was at this time that they met mergers and acquisitions expert, Morris Sullivan, who set up a corporation, Sullivan Studios to allow the trio to continue while the bankruptcy courts slowly settled their company's case against its distributor.

In 1986, Sullivan moved Goldman, Bluth & Pomeroy, and the entire operation, including 87 employees and their families to Dublin, Ireland, at the invitation of IDA Ireland. Their third feature film, The Land Before Time, was their first production created primarily in Ireland. Sullivan transferred much of the ownership of the Dublin studio to the three animators and renamed the company Sullivan Bluth Studios. The company produced six feature films from 1986 until 1994. Sullivan retired in 1991 and the company was renamed Don Bluth Entertainment, Ireland, Ltd.

In August 1994, Goldman and Bluth returned from Ireland to head up the Fox Animation Studio located in Phoenix, Arizona where they shared creative leadership as producers and Directors. The first production completed by the studio was the award-winning Anastasia in 1997. Also produced there was Bartok the Magnificent in 1999, and the animated science fiction film Titan A.E. in 2000. A fourth feature film, Africa, was in production when 20th Century Fox shut down its animation facility.

In August 2007, Goldman was named an Artist in residence at the Savannah College of Art and Design for the college's 10-week winter quarter starting in January 2008. Goldman lectured on animation, as well as taught undergraduate and graduate level classes in traditional 2-D animation production.