In 1994, Morgan was cast as the Flukeman, a mutated flukeworm the size of a human being, in "The Host", a second-season episode of The X-Files, where his brother, Glen, worked as a Writer and Producer. The episode originally aired on September 23, 1994. The role required Morgan to wear a cumbersome rubber suit for twenty hours at a stretch, an experience he described as "terrible, just horrible." Subsequently, he worked with his brother in developing the story for the next episode, "Blood" (aired September 30, 1994), for which he received story credit.

Morgan's next episode, "Clyde Bruckman's Final Repose", originally aired on October 13, 1995. "Clyde Bruckman" remains a favorite of fans and critics alike, and was acclaimed for retaining the humorous spirit of "Humbug" while extending its story into darker, more poignant territory. Both Morgan and actor Peter Boyle, who played the titular depressed psychic Clyde Bruckman, won Emmy Awards for this episode.

Morgan wrote two additional episodes of The X-Files in the 1990s: the absurdist cockroach invasion story "War of the Coprophages" (originally aired on January 5, 1996) and "Jose Chung's From Outer Space" (April 12, 1996). He also contributed to a rewrite of the episode "Quagmire" (May 3, 1996), although he was uncredited for his contributions at the time. He left the show after its third season, but joined the writing staff of Millennium, writing and directing two episodes with layered plots and humorous dialogue: "Jose Chung's Doomsday Defense" (originally aired on November 21, 1997) and "Somehow, Satan Got Behind Me" (May 1, 1998).

In addition to his work as a Writer, Morgan appeared in The X-Files episode "Small Potatoes" (April 20, 1997), playing Eddie Van Blundht, a self-described "loser" with the ability to shape-shift.

On August 11, 2004, it was announced that Morgan and Screenwriter Sam Hamm were writing an untitled screenplay under development by DreamWorks SKG. According to The Hollywood Reporter, the story "concerns a marriage counselor, whose daughter is about to get married, who discovers that his Future son-in-law is suffering from the delusion that he's a superhero."

Morgan worked as a consulting Producer on the short-lived TV reboot of Bionic Woman (2008) and Fringe (2008). He subsequently joined his brother Glen's productions of Tower Prep (2010) and Intruders (2014) as a supervising Producer, writing multiple episodes of each show.

In a March 2015 interview, Chris Carter revealed that Morgan would write an episode for the show's then-announced tenth season. The episode, entitled "Mulder and Scully Meet the Were-Monster" aired on February 1, 2016. Morgan worked on the show's eleventh season, contributing the script for the episode "The Lost Art of Forehead Sweat" (aired on January 24, 2018 ).