He began acting on the amateur stage, playing The Artful Dodger in Hessle Operatics production of Oliver! at the Hull New Theatre, also appearing in other productions including Oklahoma!, Hello, Dolly! and Joseph and the Amazing Technicolor Dreamcoat. He made his West End debut at the age of 14 in as a member of Fagin's Gang in Oliver! at the London Palladium, directed by Sam Mendes. He went on to join the National Youth Music Theatre 1996, appearing in their productions of Bugsy Malone (which transferred to the West End for a sixteen week run at the Queens Theatre in 1996), Tin Pan Ali and The Kissing Dance. He later trained at the Guildford School of Acting where obtained his BA Hons degree.

In 2003, at the age of twenty two, he was nominated for a Laurence Olivier Award for Best Actor in a Musical for his performance as Joe Casey in the Madness/Tim Firth musical Our House directed by Matthew Warchus.

Jibson's television work includes Phamer McCoy in the 2012 Primetime Emmy Awards winning 2012 US miniseries Hatfields & McCoys, directed by Kevin Reynolds and starring Kevin Costner and Bill Paxton. In 2013 BBC Four film Burton & Taylor, alongside Helena Bonham Carter and Dominic West and The Thirteenth Tale starring Vanessa Redgrave and Olivia Coleman – both for the BBC. In 2014 Tubby and Enid, directed by Victoria Wood for the BBC. In 2015 Jibson appeared as Martin Wheeler in the BBC TV series Father Brown episode 3.13 "The Paradise of Thieves" and Galavant for ABC.

In 2014, Michael co-wrote (with Paul Bryant and the films Director Chris Crow) the independent film The Lighthouse, based the tragic story of the Smalls Lighthouse in 1801. The Lighthouse is the story of two Lighthouse keepers, Thomas Howell and Thomas Griffith who were stranded on The Smalls Islands; a small cluster of rocks approximately 20 miles (32 km) west of the Pembrokeshire coast in Wales. Michael also starred as Thomas Howell opposite Welsh actor Mark Lewis Jones. The feature film was written and then selected by the Welsh Ffilm Cymru emerging talent scheme Cinematic and awarded a budget of £300,000 in conjunction with the British Film Institute (BFI), BBC Films, S4C and Soda Pictures. The film received a cinematic release in Wales and was released on DVD and VOD in 2016 in the UK, receiving positive reviews. "The Lighthouse is a welcome beacon of quality in a genre often happy to rely on cheap tricks and easy scares and offers so much more, amply rewarding those who are willing to embrace its blunt and brittle world" – Starburst'

Later in 2015 Michael gained rave reviews for portraying the English military officer Myles Standish in Saints & Strangers, a U.S. TV movie event for the National Geographic Channel and Sony Pictures. The Hollywood Reporter said – "The mini's MVP, however, is Michael Jibson as the Pilgrims' iconic military adviser, Myles Standish. His commanding performance strikes just the right balance between the mythical and the credible, as if he somehow instilled an animatronic Disneyland automaton with a stirringly virile essence". Saints & Strangers chronicled the real story of the Pilgrims: their harrowing voyage from England to America aboard the Mayflower and settling in Plymouth, Massachusetts; vying to survive in the harsh climate; their struggles with the local tribes, and celebrating their first Thanksgiving with the natives, the Pokanoket people, in 1621. It starred an ensemble including Vincent Kartheiser, Anna Camp, Ron Livingston, Barry Sloane, Brían F. O'Byrne, Natascha McElhone and Ray Stevenson. It was directed by Paul A. Edwards.

Other theatre work includes in 2004, Brighton Rock at the Almeida Theatre, playing the lead role of Pinkie Brown, directed by Michael Attenborough; in 2005–06, various roles in the Royal Shakespeare Company's adaptation of The Canterbury Tales; in 2007, Charles Lindbergh in Take FLIGHT at the Menier Chocolate Factory (nominated for a Theatregoer's Choice award for Best Supporting Actor in a Musical); in 2008, the dual roles of Puck and Philostrate in A Midsummer Night's Dream directed by Jonathan Munby at Shakespeare's Globe, where he also appeared as the Painter in Timon of Athens directed by Lucy Bailey; in 2010 he played Dromio of Syracuse in Roxana Silbert's production of A Comedy of Errors at the Manchester Royal Exchange Theatre. In 2011 he returned to the Menier Chocolate Factory where he played Addison Mizner in the European Premier of Stephen Sondheim and John Weidman's Road Show, directed by John Doyle; in 2013 he played Jimmy in Roots at the Donmar Warehouse, directed by James Macdonald. He plays the role of King George III in the West End production of Hamilton, which started previews on 6 December 2017. In April 2018 he received an Olivier Award for Best Actor in a Supporting Role for his work on Hamilton.