On television he is best known for his roles in Casualty (1997–1998), as Alan Johnson in Channel 4 sitcom Peep Show (2003–2015), Green Wing (2004–2006), Survivors (2008–2010), Boy Meets Girl (2009), as DI Wes Layton in Law & Order: UK (2013–2014), as Holy Wayne in The Leftovers (2014–2015), as DCI Mark Maxwell in Safe House (2015–2017), and as Connor Mason in Timeless (2016–2018).

Joseph is also a writer, and his 2022 debut novel The Secret Diaries of Charles Ignatius Sancho won the 2023 Christopher Bland Prize awarded by the Royal Society of Literature.

[8] In 1991, Joseph won second prize in the Ian Charleson Awards, for his 1990 performances of Oswald in King Lear, Dumaine in Love's Labour's Lost, and the Marquis de Mota in The Last Days of Don Juan, all at the Royal Shakespeare Company.

[9] In 1992, he starred as Richard Henry in Blues for Mister Charlie by James Baldwin, directed by Greg Hersov at the Royal Exchange, Manchester.

Joseph's theatre credits include the title role in Othello at the Royal Exchange, Manchester, as well as parts in Henry IV, King Lear, and Hamlet for a performance in New York City.

In 2004, he undertook a project, filmed for Channel 4 in a documentary entitled My Shakespeare, to direct a version of Romeo & Juliet, using 20 young non-actors from the deprived Harlesden area of London.

These include Reuben in William and Mary, alongside Martin Clunes; Mark Grace in Casualty; the Marquis de Carabas in Neverwhere; Alan Johnson in Peep Show; Lyndon Jones in Green Wing; and Shorty in the first episode of Jericho.

He played the messianic "Holy Wayne" Gilchrest on the original HBO dramatic series The Leftovers, which began airing in 2014, and General Arnold Gaines on You, Me and the Apocalypse.

[20] As voice actor, Joseph provided the narration for the National Geographic series Mega Cities from 2005 to 2011, Wild Russia in 2009 and the BBC Two documentary Inside Obama's White House in 2016.

Joseph appears as villain Arthur Slugworth, part of an ensemble cast in the 2023 musical fantasy film Wonka, directed by Paul King.

He voiced the character of Victor in the 2023 drama short film Bet Your Bottom Dollar[23] produced by British-Canadian filmmaker Jonathan Tammuz.

[31][32] In October 2022, Joseph was announced as the next Chancellor of Oxford Brookes University[33][34] (previous holders of the role including Helena Kennedy, Jon Snow, Shami Chakrabarti and Katherine Grainger) and was officially installed in May 2023.