Davies was born on 14 May 1968 in St Asaph, Flintshire. His Welsh parents lived in England at the time, but his father drove his mother across the border to make sure he was born in Wales so that he would be eligible to play rugby for the Welsh national team. He grew up in Wem, Shropshire, which he regards as his home. His father’s origins lie in Porthmadog. Both Davies’ paternal grandmother, Edith, and her sister, Rebecca, were illegitimate; his great-grandfather, William Owen, had a second family in Stanleytown. Like many people in North Wales, Davies also claims descent from Owain Gwynedd.

In 2005, Davies played a caricature of cricketer W. G. Grace in a series of adverts for Channel 4’s television coverage of The Ashes.

In 2007, Davies was nominated three times in the Chortle Awards, in the categories “Breakthrough Act” (for his solo stand-up act), “Best Sketch, Variety or Character Act”, and “Best Full-Length Show” (both as part of sketch team We Are Klang).

In 2010, Davies’ first solo stand-up show Firing Cheeseballs at a Dog was nominated for the Fosters Edinburgh Comedy Awards at the Edinburgh Festival. The show was subsequently taken on his first ever tour the following autumn. He was also nominated for the Edinburgh Fringe’s Malcolm Hardee “Act Most Likely to Make a Million Quid” Award.

From October 2013, Davies starred in Channel 4’s sitcom Man Down, as Dan, a man who hates his job as a teacher, with Rik Mayall as his father. Channel 4 commissioned an additional 25-minute Christmas special before the first series aired, and a second series was announced during Davies’s live tour “The Back of My Mum’s Head”, although this was before Rik Mayall’s death in June 2014. Following Mayall’s death, Davies met with Channel 4 to discuss the future of the show. Mayall had been intended to have a more a prominent role in the second series. Channel 4 later announced that Man Down would return for a second series in 2015. The classroom used in the show is the same classroom in which Davies taught at Sandhurst School.

Since July 2015, Davies has been the host of the panel game show Taskmaster. In December 2015, he starred in BBC Two’s comedy drama A Gert Lush Christmas where he played Tony, the uncle of Russell and Kerry Howard’s characters. On Christmas Day he played King Hydroflax in the 2015 Doctor Who Special “The Husbands of River Song”.

Davies is noted for his height, standing 6 ft 8 in (2.03 m) tall. He has a sister. Davies was in a relationship with Labour Party MP Liz Kendall for eight years, but the relationship ended in 2015.

In November 2017, Davies recorded a Netflix special at Hammersmith Apollo during his Magnificent Beast UK tour.

In July 2020, Davies won a BAFTA for the ninth series of Taskmaster.