Marshall was born in Madison, Wisconsin, the son of Anne and Robert D. Marshall, a professor. He was raised in Pittsburgh. His sister is the Choreographer and Director Kathleen Marshall. He graduated from Falk Laboratory School in 1974. He graduated from Taylor Allderdice High School in 1978 and was inducted into their alumni hall of fame in 2012. He attended Carnegie Mellon University and worked in the Pittsburgh theatre scene, performing with such companies as Pittsburgh Civic Light Opera.
He debuted in the film industry with the Emmy Award-winning TV adaptation of the musical Annie by Charles Strouse and Martin Charnin. After that he went on to direct the adaptation of the Kander and Ebb musical Chicago in 2002 for which he was nominated for an Academy Award for Best Director. His next feature film was the drama Memoirs of a Geisha based on the best-selling book of the same name by Arthur Golden starring Zhang Ziyi, Gong Li, Michelle Yeoh and Ken Watanabe. The film went on to win three Academy Awards and gross $162,242,962 at the worldwide box office.
In 2009, Marshall directed Nine, an adaptation of the hit Broadway production with the same name starring Daniel Day-Lewis, Marion Cotillard, Nicole Kidman, Sophia Loren and Penélope Cruz, who was nominated for an Academy Award for Best Supporting Actress. Marshall then went on to direct Pirates of the Caribbean: On Stranger Tides, the fourth chapter of Disney's Pirates of the Caribbean film series starring Johnny Depp, Ian McShane, Penélope Cruz and Geoffrey Rush, which opened on May 20, 2011.
Marshall directed Disney's film adaptation of Stephen Sondheim's Into the Woods (2014) and produced the film under his Lucamar Productions banner.
On September 14, 2015, it was announced that Marshall signed on to direct the sequel to the 1964 film Mary Poppins titled: Mary Poppins Returns, reuniting two Into the Woods actresses with Emily Blunt cast to portray the titular character and Meryl Streep in a supporting role. On December 6, 2017, it was reported that Marshall was being eyed as top choice by Disney to direct the live-action adaptation of The Little Mermaid.