Logan was born in San Diego on September 24, 1961. His parents emigrated to the US from Northern Ireland via Canada. The youngest of three children, he has an older brother and sister. Logan grew up in California and New Jersey, before moving to Chicago to attend Northwestern University, where he graduated in 1983. He was a successful playwright in Chicago for many years before turning to screenwriting. His first play, Never the Sinner, tells the story of the infamous Leopold and Loeb case. Subsequent plays include Hauptmann, about the Lindbergh baby kidnapping, and Riverview, a musical melodrama set at Chicago's famed amusement park; RED about the artist Mark Rothko that opened in London at the Donmar Warehouse and transferred to Broadway, winning the 2010 Tony Award for Best Play.

Logan currently lives in Malibu, California.

Logan wrote Any Given Sunday and the television movie RKO 281, before gaining an Academy Award nomination for co-writing the Best Picture-winner, Gladiator in 2000. He gained another nomination for writing 2004's The Aviator, starring Leonardo DiCaprio and directed by Martin Scorsese. Other notable films written by Logan include Nemesis, The Time Machine, The Last Samurai, and Tim Burton-helmed musical, The Demon Barber of Fleet Street. He also wrote a script for I Am Legend, which was to be directed by Ridley Scott, but that project collapsed and was never produced.

His play Red about artist Mark Rothko, was produced by the Donmar Warehouse, London in December 2009 for two months, and on Broadway, where it received six Tony Awards in mid-June, 2010, the most of any play, including best play, best direction of a play and best featured actor in a play for Eddie Redmayne. Redmayne and Alfred Molina had originated their roles in London and brought them to New York for a limited run ending in late June.

Logan's future projects include Rango, an animated feature about a lizard, and Bioshock, based on the popular video game for Universal Pictures. He also wrote the upcoming film Empire which will be directed by Michael Mann and will star Will Smith. Logan is also writer of the new HBO drama “Miraculous Year,” which is expected to include a role for Eddie Redmayne. He wrote the script for the upcoming The Passage film adaption.