Born in Los Angeles, California, he is the youngest son of Martha Louis Montgomery (1920–2005) and Composer Alfred Newman (1900–1970), who won the Academy Award for Best Original Score nine times. He is a member of a film-scoring dynasty in Hollywood that includes his father Alfred, brother David Newman, sister Maria Newman, uncles Lionel Newman and Emil Newman, cousin Randy Newman (also known as a singer and songwriter), and his first cousin, once removed, Joey Newman. His paternal grandparents were Russian Jewish immigrants, and his mother was from Mississippi.

During their upbringing, Martha herded her sons into violin lessons in the San Fernando Valley every weekend. Newman later studied composition and orchestration for two years at the University of Southern California, before transferring to Yale University, where he graduated as a Bachelor of Arts in 1977 and a Master of Music in 1978. While at Yale, he met Composer Stephen Sondheim, who became an early mentor.

At first, Newman was more interested in musical theater than in film composition, working with Sondheim in Broadway plays. Lionel, who succeeded Alfred as music Director for 20th Century Fox, gave Thomas his first scoring assignment on a 1979 episode of the series The Paper Chase. In 1983, John Williams, who was a friend of both Alfred and Lionel, invited Newman to work on Return of the Jedi, orchestrating the scene where Darth Vader dies. Afterwards Newman met in New York Producer Scott Rudin, who invited him to compose the score for Reckless (1984). Newman said that he thought "it was a tough job, at first" for requiring him to "develop vocabularies and a sense of procedure", only getting comfortable with writing scores "and not fraudulent in my efforts" after 8 years.

In 1992, Newman composed the score to Martin Brest's film Scent of a Woman.

His first major successes for which he was recognised, came in 1994, when he earned two Academy Award nominations for his scores to Little Women and The Shawshank Redemption; he was the only double-nominee that year, although he lost to Hans Zimmer for The Lion King.

He received his third Academy Award nomination in 1996 for the score to Diane Keaton's comedy Unstrung Heroes, but again lost, this time to Alan Menken for Pocahontas.

He has also received three Golden Globe nominations including one for Best Original Score for 1999's American Beauty and two for Best Original Song, as well as nine Grammy nominations and five wins.

Newman has been nominated for fourteen Academy Awards and three Golden Globes, and has won two BAFTAs, six Grammys and an Emmy Award. Newman was honored with the Richard Kirk award at the 2000 BMI Film and TV Awards. The award is given annually to a Composer who has made significant contributions to film and television music.

His critical and commercial success has continued in the following years with his scores for films such as Meet Joe Black, The Green Mile, Erin Brockovich, In the Bedroom and The Salton Sea. He was nominated consecutively for a further three Academy Awards, for Road to Perdition (2002), Finding Nemo (2003), and Lemony Snicket's A Series of Unfortunate Events (2004). However, he lost on each occasion to Elliot Goldenthal (for Frida), Howard Shore (for The Lord of the Rings: The Return of the King), and Jan A. P. Kaczmarek (for Finding Neverland) respectively.

Newman has composed music for television as well, including theme music for the series Boston Public and the miniseries Angels in America. His theme music for the television show Six Feet Under won two Grammy Awards in 2003, for Best Instrumental Composition as well as Best Instrumental Arrangement. Newman also wrote a commissioned concert work for orchestra, Reach Forth Our Hands, for the 1996 Cleveland Bicentennial. The Los Angeles Philharmonic has commissioned a new work by Newman to be performed by the Kronos Quartet and Los Angeles Philharmonic, conducted by Leonard Slatkin, during the orchestra's 2009–2010 season.

He was again nominated for an Oscar for scoring Steven Soderbergh's The Good German (2006). At the Oscar ceremony, he appeared in the opening segment by Errol Morris, who jokingly stated that Newman had been nominated for and failed to win an Oscar eight times. Newman replied: "No, I've failed seven but this will be my eighth", and indeed, he again lost, this time to Gustavo Santaolalla for Babel.

In 2008, Newman scored Towelhead and Sam Mendes' Revolutionary Road and in 2009 he scored Brothers. In 2011 he scored The Help, The Debt, The Iron Lady, and The Adjustment Bureau.

In 2012, Newman scored The Best Exotic Marigold Hotel. He also scored the 23rd James Bond movie Skyfall, directed by his longtime collaborator Sam Mendes, which celebrates the film franchise's 50th anniversary. His work on this film earned him his eleventh Oscar nomination and a second BAFTA win. During 2013, he scored Steven Soderbergh's Side Effects and Saving Mr. Banks. The latter score was very well received by film music critics, earning Newman BAFTA and Oscar nominations for the second consecutive year, both of which he lost to Steven Price for Gravity.

He composed the incidental music for the Washington Shakespeare Theatre Company's 2014 production of As You Like It, directed by Michael Attenborough and starring Zoe Waites.

In 2016, Newman scored the motion picture Passengers starring Jennifer Lawrence and Chris Pratt.

As of 2017, Newman has received a total of fourteen Academy Award nominations, however he has yet to win the award, making him the most nominated living Composer to have never won an Oscar, and behind Alex North, who received 15 unsuccessful nominations. Thirteen of his nominations are in the Best Original Score category, while one is for Best Original Song.