Boyd began acting at age 17 in amateur theatre and performed in local productions from 1989 to 1995. Boyd moved to London in his mid-20s, where he continued to work in theatre until being cast in 'Kiss Me Kate' for the BBC in 1992.
Boyd co-starred in the BBC comedy Kiss Me Kate (1998), which ran for three years. This led to starring roles in British comedies such as Hippies (1999) and Smack the Pony (1999). In 2001, he collaborated with Victoria Pile on a new series Los Dos Bros, an off-beat sitcom exploring physical comedy and the relationship between Boyd and Cavan Clerkin as the titular (half-)brothers. Boyd was co-creator and co-writer. The show won a silver rose at Montreux in 2002. During this time Boyd was cast in the American NBC series, Watching Ellie, starring Julia Louis-Dreyfus.
Feature films in which Boyd has appeared include High Heels and Low Lifes (2002), Imagine Me & You (2005), Magicians (2007), Chris Morris' Four Lions (2010), The World's End (2013), Alan Partridge: Alpha Papa (2013) and Thomas & Friends: Journey Beyond Sodor (2017).
Boyd returned to the UK in 2005 and took on characters such as Dr. Jake Leaf in the second series of Green Wing (2006), and as Jonathan in Steve Coogan's Saxondale. In 2009, he appeared in the two-part adaptation of May Contain Nuts, based on John O'Farrell's best-selling novel, Personal Affairs for BBC Three and Royal Wedding (2010), which follows the 1981 Royal Wedding through the perspective of events held in a small Welsh mining village, written by BAFTA winner Abi Morgan and starring Jodie Whittaker.
From 2011-2013, Boyd starred in the Sky 1 series Spy which won him a BAFTA for his performance. He's also starred in two ITV dramas, Case Sensitive, a series adapted from Sophie Hannah's novel Point of Rescue alongside Olivia Williams and three-part drama The Guilty.
In 2014, Boyd reunited with his Watching Ellie costar Julia Louis-Dreyfus in a guest appearance on her HBO series Veep in the episode "Special Relationship".
Boyd was part of the ensemble cast of Sky Atlantic drama series Fortitude, which premiered simultaneously in the UK and US in early 2015. He won praise from critics and audience alike for playing Markus Huseklepp, the immensely creepy feeder, which was a turn from the likable, comedy characters that he is otherwise known for. Following Fortitude, Boyd briefly returned to comedy in the lead role of Matthew Bunton in the ITV situation comedy The Delivery Man.
In 2016, he returned to television with two dramatic roles. He starred opposite Idris Elba in the fourth series of Luther for the BBC and James Nesbitt in Stan Lee's Lucky Man, a Sky 1 television series.
