Walsh, a trained dancer from childhood, made his Broadway debut in 1973 in Seesaw; that same year, he appeared in the film version of Jesus Christ Superstar. In 1975, he bowed as Bobby in A Chorus Line, first at The Public Theater and then on Broadway. He later co-wrote the book On the Line, which detailed the show's creation.
In the late 1970s, Walsh changed his focus to choreography. Over the next decade, he worked with his old friend and Seesaw co-star Tommy Tune on a number of Broadway shows, including The Best Little Whorehouse in Texas, A Day in Hollywood/A Night in the Ukraine, Nine, and My One and Only. The latter show earned Walsh his second Tony for Best Choreography -- his first was for A Day in Hollywood -- along with a Tony nomination for Best Direction. His final Broadway show was in 1992, when he created the musical staging for the short-lived My Favorite Year.
Walsh's many other credits included directing the original Off-Broadway production of Lucky Stiff, creating cabaret and nightclub acts for performers such as Donna McKechnie, directing many editions of the MAC Awards, directing and choreographing the 1999 national tour of Best Little Whorehouse starring Ann-Margret, and choreographing the Off-Broadway musical A Woman of Will, starring Amanda McBroom.