Davies was born in St Asaph, Denbighshire. His parents lived in England at the time, but his Welsh father drove his mother Pauline across the border to make sure he was born in Wales. He grew up in Wem, a small market town in the northern half of Shropshire, the county which he regards as his home. He also has a sister.
Davies was educated at Thomas Adams School and Brunel University, where he studied English and Drama. Prior to embarking on a career in comedy, he had taught secondary school Drama and English for thirteen years at Langleywood School in Slough, Orleans Park School in Twickenham, southwest London, and Sandhurst School in Sandhurst.
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.
In December 2015 Davies 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"
From July 2015 Davies has been the host of the Dave show Taskmaster.
Davies is noted for his height, standing 6 ft 8 in (2.03 m) tall and has size 13 feet.
He was previously in a relationship with Liz Kendall, a Labour politician who, in 2015, was re-elected as the Member of Parliament for Leicester West. However, the couple split up just a few months prior to the 2015 General Election.
In February 2017, Davies was the subject of a programme in the BBC genealogy series Who Do You Think You Are? In the programme Davies returned to his father's family origins in Porthmadog, North Wales and discovered that both his paternal grandmother, Edith, and her sister, Rebecca, were illegitimate. His great-grandfather William Owen had a second family who were brought up in Stanleytown in the Rhondda Valley, South Wales. Like many people in North Wales, Davies also claimed descent from Owain Gwynedd.