Linn-Baker began his career on the stage, coming to New York after working three seasons with the Yale Repertory Theater. He made his NY stage debut as Bertram in a New York Shakespeare Festival production of "All's Well That Ends Well", went on to garner favorable notices for starring roles in a number of festival productions, and then made his Broadway debut in "Doonesbury", a short lived musical based on the popular comic strip.
Linn-Baker had his big screen break-through opposite Peter O'Toole in the very successful comedy "My Favorite Year" (1982), as a young 1950s variety show writer who has to chaperon that week's star, a known drunk and womanizer (O'Toole). It would be a decade before Linn-Baker worked on the big screen again, co-starring in Peter Bogdanovich's "Noises Off" (1992). Meanwhile, he worked in episodic TV, landed regular roles on a summer series "The Comedy Zone" (1984) and made a busted pilot "The Recovery Room" (1985) before being cast in "Perfect Strangers". During the years he starred on the series, Linn-Baker showed up periodically on awards shows, specials and starred in such TV-movies as "Wedding Day Blues" (1988) and "Bare Essentials" (1991).
In the late 1980s, Linn-Baker co-founded the New York Stage & Film Company which produced plays and short films. The company developed Jay Presson Allen's "Tru" a one man show about the life of writer Truman Capote that eventually moved to Broadway. Linn-Baker also directed regional and off-Broadway productions of plays by Christopher Durang and John Patrick Shanley, as well as TV episodes of "Going Places", "Hangin' With Mr. Cooper" and "Family Matters".
In the mid-90s, he returned to the NY stage co-starring with Nathan Lane in Neil Simon's "Laughter on the 23rd Floor" (1993-94), based on Simon's experiences as a writer for the TV series "Your Show of Shows". Three years later, he and Lane teamed again for the revival of the Larry Gelbart-Burt Shevelove-Stephen Sondheim musical "A Funny Thing Happened on the Way to the Forum". Linn-Baker played Hysterium, a slave who agrees to help a friend by posing as a virginal young woman.
Linn-Baker is married to theatrical set designer Adrianne Lobel.