Kitson was born in Denby Dale, West Yorkshire to a lecturer father and primary school head teacher mother,and began performing comedy at the age of 16. He was a pupil at Scissett Middle School and Shelley College in Yorkshire, England. Kitson subsequently studied drama at Roehampton Institute, now known as Roehampton University.
He was nominated for the 2001 Perrier Comedy Award at the Edinburgh Festival Fringe for his show Love, Innocence and the Word Cock before winning it in 2002 for the show Something.
As well as stand up, Kitson has written and performed "story shows". The first was A Made Up Story at the 2003 Edinburgh Festival Fringe, followed by Stories For the Wobbly-Hearted at the Melbourne International Comedy Festival in 2005. The latter show opened at the Traverse Theatre for the 2005 Edinburgh Festival Fringe and won a Scotsman Fringe First Award. In 2006, Kitson took Stories For The Wobbly Hearted to the Brits Off Broadway Festival in New York.In June 2006 the story show made up one half of his Regents Park Open Air Theatre appearance, where Kitson's stories were accompanied by songs from Gavin Osborn. His story show, C-90, opened at the Traverse for the 2006 Edinburgh Festival Fringe. It was awarded both a Fringe First and The Stage Acting Award for Best Solo Show.
In 2007, Kitson toured It's The Fireworks Talking and the story show C-90 in the UK, Australia, New York and Paris. There was a second Open Air Theatre show in June 2007. Kitson also complemented his Australian tour of C-90 with a loosely structured stand up show titled At 10PM, Daniel Kitson Will Be Drinking Tea and Blowing Minds, a reference to a line from the movie Dazed and Confused.
It's The Fireworks Talking won Kitson the Barry Award - named after veteran Australian comedian Barry Humphries - at the 2007 Melbourne International Comedy Festival. C90 was awarded an Argus Angel Award at the 2007 Brighton Festival.
In the first half of 2008 Kitson toured his show The Impotent Fury of the Privileged. He played work-in progress gigs in January and early February before presenting the show at 28 dates during May & June. In July 2008 he began previews of his Edinburgh Festival show, 66A Church Road: A Lament, Made Of Memories And Kept In Suitcases.
In 2009 Kitson performed two new shows: 'We Are Gathered Here' & 'The Interminable Suicide of Gregory Church', the latter of which was toured in late 2010 and the first half of 2011. Prior to this in early 2010, Kitson also did a short UK tour of '66a Church Road - A Lament Made of Memories and Kept in Suitcases' that he initially performed in Edinburgh in 2008 (and then took to Australia.)
In January, 2012, his show "It’s Always Right Now, Until it’s Later" played at the St. Ann's Warehouse in Brooklyn, NY.
In March 2012, Kitson took a brand new stand-up show, Where Once Was Wonder, on a work-in-progress tour around the UK before touring it in Australia and returning for the Edinburgh Fringe in August. The new show comprises all new material and is made up of three stories about "the impossible".