A graduate of the University of Arizona's College of Architecture, Welch began a promising career as an architect in Los Angeles. Like fellow production designer Joseph Nemec III, he answered an advertisement for work at Universal Studios and soon found work as a set designer. Welch gained his first screen credit for his efforts on Robert Zemeckis' "Used Cars" and Walter Hill's period Western "The Long Riders" (both 1980). After further work as a set designer on films like "Mommie Dearest" and Mel Brooks' "History of the World Part I" (both 1981), he graduated to art director on Jonathan Demme's "Swing Shift" (1984). He shared in the Oscar nomination for the design of Steven Spielberg's "The Color Purple" (1985), which recreated Southern life in the first four decades of the Twentieth Century.
Welch subsequently provided the eye-catching contemporary settings for Joel Schumacher's slick vampire tale "The Lost Boys" (1987) and began a fruitful collaboration with Tim Burton on "Beetlejuice" (1988). In the latter, Welch created a haunted house as well as the ghostly world inhabited by the title character. He designed the contemporary settings for Lawrence Kasdan's "The Accidental Tourist" (1988) and Ivan Reitman's "Ghostbusters II" (1989). Welch's flair for the fantastic was highlighted by two further Burton films. In "Edward Scissorhands" (1990), he created an eerie deserted mansion that was home to Edward as well as the colorful suburban community (that evoked the 50s) to which Edward is transplanted. For "Batman Returns" (1992), the designer and the director re-interpreted the dark version created by Anton Furst for "Batman" (1989). Welch fashioned a somewhat more generic, yet densely overbuilt and dehumanizing metropolitan look.
Welch earned his second Oscar nod for his beautifully detailed Edwardian designs for Alfonso Cuaron's remake of "A Little Princess" (1995). The look of this film was particularly important and Welch's contribution was to recreate a variety of settings, ranging from colonial India to the world of the girl's imagination to a girls boarding school in World War I-era New York. The following year, Welch again was tapped by the Academy, this time for his flashy contemporary settings for Mike Nichols' "The Birdcage", creating a world where showbiz artifice and reality overlap in South Beach, Florida. He followed with Oscar-nominated work on the sci-fi comedy "Men in Black" (1997) and its less-honored sequel (2002), along with design on the biting political comedy "Primary Colors" (1998), the leaden film adaptation of "Wild, Wild West" (1999) and Garry shandling's semi-sci-fi comedy "What Planet Are You From?" (2000).
With a litany of design triumphs to his credit, Welch ventured into a second career as a director, making his debut on an episode of the short-lived Barry Josephson/Barry Sonnenfeld spy spoof TV series "Secret Agent Man" (2000) followed by episodes for another Josephson/Sonnenfeld effort, the comic book satire "The Tick" (Fox, 2001-2002), for which Welch also created the pilot's production design. His feature debut came with the live-action adapation "Dr. Seuss' The Cat in the Hat" (2003), which was predictably filled with inspired production design details but came up lacking on story and character charm.