His mother, Joan (née Sparks), of Jewish ancestry, was a dancer, and his father, William Nelson Baker, co-founded the Open Stage Theater in Hartford.

He appeared in Laughter on the 23rd Floor in 1993; the 1996 revival of A Funny Thing Happened on the Way to the Forum; the 1998 Roundabout Theatre Company production of A Flea in Her Ear; the 2003 musical A Year with Frog and Toad; and the 2006 comedy Losing Louie.

In a manner similar to his future role in Perfect Strangers, Linn-Baker played the straight man to O'Toole's outrageous character, Alan Swann.

Linn-Baker starred with Charles Kimbrough in the 1985 CBS pilot The Recovery Room, a sitcom about a bar located across from a major city hospital and its inhabitants.

Between parts, Linn-Baker also appeared during this time in television commercials pitching products ranging from Kellogg's Nutri-Grain to Kraft's Life Savers.

Linn-Baker starred in the ABC series Perfect Strangers as Larry Appleton, a young man living on his own for the first time in Chicago.

Larry's world was disrupted when a distant cousin from the (fictional) Mediterranean island of Mypos, Balki Bartokomous (Bronson Pinchot), showed up on his doorstep.

[5] As of 2017 he is playing the role of Carlton Miller, aide to Mayor Margaret Dutton (Lorraine Bracco) on the CBS police procedural drama Blue Bloods.

In 2019, he played Mayor George Shinn in the Kennedy Center's production of The Music Man opposite Norm Lewis as Hill and Jessie Mueller as Marian.

He reprised his role when he replaced Jefferson Mays in the 2022 Broadway revival, where he performed opposite Hugh Jackman as Hill and Sutton Foster as Marian.

On a 2003 episode of Law & Order: Criminal Intent, he guested as an insurance investigator named Wally Stevens who displays strong Asperger's Syndrome traits.

In 2010, he appeared in an episode of Law & Order, "The Taxman Cometh", as Dr. Vincent Balicheck, a physician who used controversial therapies on cancer patients which resulted in their deaths.

[7] Linn-Baker and Perfect Strangers are referenced in the HBO TV series The Leftovers, which takes place after a fictional global event called the Sudden Departure, the inexplicable, simultaneous disappearance of 140 million people, 2% of the world's population.