Newman was born in Glasgow. His father is Sandy Newman, a member of Scottish band Marmalade. He has a brother named John, who appeared on The Voice UK in 2012. Prior to joining the National Youth Theatre in London at age 17, Newman considered becoming a professional footballer. He trained at the London Academy of Music and Dramatic Art.
Newman starred as Paul Atreides in the Sci Fi Channel's 2000 miniseries adaptation of Frank Herbert's Dune and reprised the role in its 2003 sequel Children of Dune. He has had guest appearances on U.S. television series Angel, Star Trek: Enterprise and Tru Calling. He also guested on the British spy drama Spooks and played the Rebus-inspired Jim Buchan in BBC 4's Reichenbach Falls. He took the title role of Victor Frankenstein in the 2004 Frankenstein US TV miniseries, opposite Donald Sutherland and William Hurt.
On film in the UK, Newman played the lead role in Penny Woolcock's 2003 The Principles of Lust, nominated for a British Independent Film Award and selected for competition at the Sundance Film Festival. Other British films include Long Time Dead for Working Title, G:MT produced by Taylor Hackford, and Stephen Fry's Bright Young Things.
In 2004, he landed the role of Barnabas Collins in a pilot for a revival series of Dark Shadows on the WB Network.
Other films in the US include Four Corners of Suburbia, Constellation, and the Lions Gate release The Gene Generation. An attempt at an old style Hollywood musical, Moonlight Serenade starred Alec opposite Amy Adams.
Newman starred in the short-lived BBC One series Hope Springs in 2008. He also played the recurring role of Robert Ludlow in Casualty for a run of 10 episodes in 2010 as well as guesting in a Silent Witness two-parter entitled "Run".
The same year Newman starred with Sean Harris and Melissa George in Julian Gilbey's action-oriented A Lonely Place to Die.
In 2010/11 he played Edmund in the Donmar Warehouse production of Shakespeare's King Lear. The production subsequently toured the UK and played a six-week engagement at the Brooklyn Academy of Music (BAM) in Brooklyn, New York. This followed massive critical success in the National Theatre's production of Danton's Death, in which Newman portrayed the powerful, persuasive Saint Just. Both productions were directed by Michael Grandage.
On 30 May 2011, it was announced that Newman had joined the cast of BBC One drama series Waterloo Road in the role of the new head teacher, Michael Byrne. He completed series 7 and 8 as the character, leaving the show in early 2013, after its relocation to Greenock in Scotland.
In early 2013, he became an ambassador for the Blind Veterans UK charity, to help them reach 68,000 blind veterans unaware of the assistance the charity can provide. This was in conjunction with his portrayal of Mal Walker, a blind veteran of Afghanistan in the feature film Greyhawk, directed by Guy Pitt.
In August 2013, he began work on Season 2 of Directv's series Rogue. The series aired in 2014.
Other American television appearances include the 2013 NBC series Dracula, and a recurring role in 24: Live Another Day. He subsequently appeared in the BBC America series The Last Kingdom.
This was followed with a series role in Kurt Sutter's short lived FX show The Bastard Executioner, shot in Wales. He then returned to the National Theatre, playing Ralph in the acclaimed Indhu Rubisingham production of The Motherfucker with the Hat at the Lyttelton Theatre. He also starred in Hampstead Theatre's 2015/16 production of Stoppards "Hapgood".
He regularly lends his voice to high-profile video games, commercials and documentaries for the BBC and Discovery Channel.
He has voiced Jack the Ripper in Assassin's Creed: Syndicate- Jack the Ripper DLC and Gabriel Angelos in Warhammer 40,000: Dawn of War III.
He filmed a role in Tomas Alfredson's The Snowman, before an appearance in Simon Evans production of Tracy Letts "Bug" at Found 111. This was followed by a second collaboration with Evans, this time in the World Premiere of Andrew Keatley's "Alligators" at Hampstead Theatre in June 2016. Newman returned to play Daniel Turner in 'Alligators' when the play was revived Downstairs at Hampstead Theatre in June 2017.
Roles in ITV series HIM and Fearless (the latter by Homeland scribe Patrick Harbinson) followed.
In February 2013, Newman became engaged to Heather Stewart. They married in Ayrshire in June 2014.