While working in theater, Burrows wrote Moore and her then husband Grant Tinker seeking a job at their production company, MTM Enterprises. In 1974, Tinker hired Burrows as a Director for MTM Enterprises where he directed episodes of The Mary Tyler Moore Show and The Bob Newhart Show. Tinker asked Director Jay Sandrich, known for his work directing The Mary Tyler Moore Show and later The Cosby Show and The Golden Girls, to serve as a mentor to Burrows.

Burrows co-created Cheers with brothers Glen and Les Charles. The Charles brothers were also former employees of MTM Enterprises and served as producers on the series Taxi where Burrows worked as in house Director for 76 episodes. Burrows and the Charles brothers wanted to create a show where they could have more control. Cheers premiered on NBC on September 30, 1982. Although Cheers initially struggled in the ratings, the series became a hit, running 275 episodes over eleven seasons. Burrows directed all but 35 of those 275 episodes.

In 1998, Burrows directed a Chicago-based production of the 1939 comedy The Man Who Came to Dinner starring John Mahoney.

Burrows has had cameo appearances in several of the shows for which he has directed. In the first season of Friends, Burrows appeared in the episode "The One with the Butt" as the Director of the film in which the character Joey Tribbiani is cast as Al Pacino's "butt double". He also appears as a television Director named Jimmy in the 2005 HBO series The Comeback. Burrows played himself on the series. An episode of Scrubs, "My Life in Four Cameras", had a character named Charles James in honor of Cheers creators Burrows and Glen and Les Charles. It was previously asserted in Sitcoms: the 101 Greatest TV Comedies of All Time (2007) that Burrows served as the silhouette of the customer who knocks on the door in the final scene of Cheers, but Burrows himself refuted this claim on episode 9 of the NewsRadio-themed podcast Dispatches from Fort Awesome, revealing that the actual "Man Who Knocks" was agent Bob Broder.

Burrows directed every episode of Will & Grace during its initial eight-year run. Additionally, by 2012 Burrows had directed over 50 pilots for television series.

Over the course of his career, Burrows has been nominated for fifteen Directors Guild of America awards, and for an Emmy Award every year between 1980 and 2005, excluding 1997. Burrows has won ten Emmy Awards and four Directors Guild of America Awards. The Academy of Television Arts and Sciences celebrated Burrows' forty-year career by hosting a panel in his honor on October 7, 2013.

Burrows has directed over 1,000 episodes of television, a milestone he achieved in November 2015 with the NBC sitcom Crowded. To celebrate Burrows' achievement, NBC aired a special tribute on February 21, 2016, titled Must See TV: An All-Star Tribute to James Burrows featuring cast reunions from many of the series Burrows has directed such as Cheers, Taxi, Friends, Frasier, The Big Bang Theory, Will & Grace and Mike & Molly.

Burrows was born to a Jewish family in Los Angeles, California, the son of Ruth (Levinson) and Abe Burrows, a well-known Composer, Director and Writer. James has one sister, Laurie Burrows Grad. When James was still a young child, his family moved to New York where James attended New York’s High School of Music & Art. Burrows is a graduate of Oberlin College and the graduate program of the Yale School of Drama.