Ellis graduated from Goodman School of Drama at the Art Institute of Chicago (now at DePaul University) in Chicago. He also graduated from James W. Robinson Secondary School, in Fairfax, Virginia, in 1975. He studied acting at HB Studio in New York City. Ellis has a twin brother named Mark Ellis, who is the Executive Director of the International Bar Association.
Before he became a director, Ellis was a successful stage actor; he performed on Broadway in the original casts of the 1980 original musical Musical Chairs and The Rink with Liza Minnelli and Chita Rivera.
He has directed numerous Off-Broadway and Broadway productions, as well as the New York City Opera Company revivals at the New York State Theater of A Little Night Music (1990) and 110 in the Shade (1992).
Ellis has been the Associate Artistic Director for the Roundabout Theatre since 1998.
He has been nominated for the Tony Award as Best Director nine times for a revival of She Loves Me (1994), Steel Pier (1997), a revival of 1776 (1998), Twelve Angry Men (2005), Curtains (2007), a revival of The Mystery of Edwin Drood (2013), a revival of You Can't Take It with You (2015), another revival of She Loves Me (2016), and Tootsie (2019). He received the 1991 Drama Desk Award, Outstanding Director of a Musical, for And The World Goes Round. He won the Olivier Award as Best Director, Musical, for She Loves Me.
He was the executive producer for the television drama Weeds on Showtime, and has directed television episodes of Modern Family, Nurse Jackie, The Good Wife, Hung, 30 Rock, Desperate Housewives, The Closer and Frasier. He received an Emmy Award nomination in 2007 for directing the episode "The Break-Up" of the comedy series 30 Rock.
In 2010, Playbill announced that Ellis was expected to direct upcoming musical adaptations of the 1930s films The Blue Angel and Little Miss Marker. Both would have books by David Thompson.
He played the role of Leonard Bernstein's manager Harry Kraut in the biopic Maestro (2023).
