Edmondson, the second of four children, was born in Bradford, West Riding of Yorkshire to Dorothy Eileen Sturgeon and Fred Edmondson (1929-2014). As a child, he lived with his family in a variety of places including Cyprus, Bahrain, and Uganda, where his father was a Teacher in the armed forces. In the mid-1980s, his father became the deputy headmaster at the former Drummond Middle School in Manningham, Bradford. Edmondson attended Pocklington School, East Riding of Yorkshire from 1968 to 1975. In an interview with the Times Educational Supplement, he stated that he did not enjoy his education at Pocklington.
Under the name 20th Century Coyote, Edmondson and Mayall became one of the star attractions at The Comedy Store. As their popularity grew, Edmondson, Mayall and other upcoming comedians, including Nigel Planer, Peter Richardson, Alexei Sayle, and French and Saunders moved from the Comedy Store to The Comic Strip club. The Comic Strip soon gained a reputation as one of the most popular comedy clubs in London and soon came to the attention of Channel 4. Edmondson and the others were commissioned to act in 6 self-contained half-hour films, using the group as comedy actors rather than stand-up performers. The series, entitled The Comic Strip Presents... debuted on 2 November 1982 (the opening night of Channel 4). The first episode to be broadcast was "Five Go Mad in Dorset", a parody of Enid Blyton's Famous Five, which drew anger from some viewers for the way it mercilessly satirised a children's classic. Edmondson starred as one of the five.
In 1984, Edmondson formed the spoof Heavy Metal band Bad News as part of The Comic Strip Presents... series with Comic Strip regulars Rik Mayall, Nigel Planer and Peter Richardson. The band proved popular, and they released two singles (neither of which reached the top 40) and two studio albums. They also played a series of small gigs around the country, culminating in their performance at the Monsters of Rock festival in 1986.
On 11 May 1985, Edmondson married fellow Comic Strip actor Jennifer Saunders, with whom he has three daughters: Eleanor, Beatrice, and Freya. Edmondson's university nickname of "Eddie Monsoon", a play on his surname, inspired the name of Saunders' character, "Edina Monsoon" in Absolutely Fabulous and his own characters "Eddie Catflap" (Filthy Rich & Catflap) and "Eddie Hitler" (Bottom). Edmondson and Saunders jointly established their own production company called "Mr and Mrs Monsoon Limited". Also in 1985 Edmondson starred with Saunders in Happy Families, a rural comedy drama written by Ben Elton which appeared on the BBC and told the story of the dysfunctional Fuddle family.
In 1986, Edmondson achieved a number one hit in the UK singles charts when he and his co-stars from The Young Ones teamed up with Cliff Richard to record a new version of "Living Doll" for the inaugural Comic Relief campaign. Despite having been killed off in the final episode of the series, Edmondson played Vyvyan one last time in the video. The same year he co-wrote the book How to be a Complete Bastard together with Mark Leigh and Mike Lepine.
In 1987 Edmondson reunited with Planer and Mayall to star in Filthy Rich and Catflap, a comic attack on showbiz, again written by Elton. He played "Edward Catflap", a coarse, drunken minder of light-entertainment nonentity "Richie Rich". In this show Edmondson displayed the same slapstick characteristics as Vyvyan in The Young Ones but was closer in personality to his later character "Eddie Hitler" in Bottom. The show received critical acclaim but poor viewing figures and was cancelled after one series. Edmondson also co-starred in 1987 with Mayall in the ITV sit-com Hardwicke House. Due to the adverse reaction of both press and viewers, however, ITV withdrew the series after two episodes and the remaining episodes have never been shown. In 1988, he released a follow up to How To Be A Complete Bastard called The Bastard's Book of the Worst. In 1989 he made an appearance in an episode of Blackadder Goes Forth as The Red Baron, nemesis to Mayall's character, Lord Flashheart.
Edmondson has directed pop videos for "Fiesta" (1988) by The Pogues, "Prime Mover" (1987) by Zodiac Mindwarp, "Like The Weather" (1988) by 10,000 Maniacs, "Please Help The Cause Against Loneliness" (1988) by Sandie Shaw and "Hourglass" by Squeeze (1987). He appeared in the music videos to Terry by Kirsty MacColl and International Rescue by Fuzzbox.
In 1991, Edmondson formed The Bum Notes, who were a jazz instrumental band and conceived exclusively to perform theme music for Bottom.
Following the 1997 Bottom stage tour, Hooligans Island, Mayall and Edmondson worked on the idea of a Bottom film in which Richie and Eddie run a hotel. The two had been working on the script together and were set to co-direct. In 1998 Mayall was seriously injured and spent five days in a coma. Edmondson found this time very difficult. When Mayall came around he helped Edmondson complete the script while still in hospital. The film became Guest House Paradiso. In December 2004 the Daily Mirror newspaper quoted Edmondson as saying: "It's definitely time to stop. We're getting too old. We both realised that the show wasn't as engaging as it used to be. We were starting to look a bit ridiculous. [...] We're both nearly 50 and we're starting to feel slightly undignified talking about wanking and knobs constantly." Rik Mayall repeatedly said that they would work together again, they just needed "a good idea."
Edmondson appeared regularly as Brendan Baxter in Series 4 of the BBC mystery series Jonathan Creek, broadcast in 2003–2004. He had a lead role playing an NHS Doctor in the comedy series Doctors and Nurses first broadcast in early 2004. In Surviving Disaster, a BBC docudrama about the 1986 Chernobyl disaster, broadcast at the start of 2006, Edmondson played the role of Dr Valery Legasov. In 2005 he appeared as a Celebrity model on Star Portraits with Rolf Harris. That year, he also competed on "Comic Relief Does Fame Academy" where he made it to the finale and came in 3rd place. From 2005 to 2008 he appeared as Percy "Abra" Durant in the medical drama Holby City. In 2008 he played Henry Austen in the BBC produced film Miss Austen Regrets and Vernon in the ITV sitcom Teenage Kicks. In April 2009 he appeared on the cooking show Hell's Kitchen, where he reached the final, coming second to Linda Evans.
A fan of the Bonzo Dog Doo Dah Band, Edmondson performed vocals with them as part of their 2006 reformation and countrywide tour. He also contributed vocals and writing for their 2007 album Pour l'Amour des Chiens.
In 1993, Edmondson starred alongside Richard Briers in a black comedy called If You See God, Tell Him. Edmondson played Gordon Spry, whose uncle (Briers) is paralysed and has a greatly reduced attention span. His erratic behaviour causes problems for Gordon. The series comprised four episodes, each 45 minutes long, and only broadcast once. The BBC has not repeated the series, although one episode was broadcast on BBC Four on 3 December 2007. Since 1993 Edmondson has been voicing The Animal in adverts for Peperami. September 1995, Edmondson released his first (comic) novel, The Gobbler. In 1996, he played the role of Ace Face/Bellboy at The Who's performance of Quadrophenia at London's Hyde Park. A video game called Animal, featuring Peperami's "the animal", was released the same year, with the character being voiced by Edmondson. From 1997 to 1998 he voiced engine stoker Jones, a major character in the animated series Captain Star. In the 1998 ITV pantomime Jack and the Beanstalk, Edmondson played Jack's mother Dame Dolly alongside Neil Morrissey, Denise Van Outen, Paul Merton, Julian Clary and Julie Walters.
Together with Maartin Allcock, Andy Dinan and Troy Donockley, Edmondson founded the band The Bad Shepherds in 2008, performing punk and new wave classics on traditional folk instruments. The band have released three albums and first toured in 2009, playing at places such as the Trowbridge Village Pump Festival. The Bad Shepherds also headlined the first ever Looe Music Festival in 2011.
Edmondson played the role of Captain Hook in the Canterbury Marlowe Arena pantomime during its Christmas 2009 run.
In 2010 he founded The Idiot Bastard Band with Simon Brint, Rowland Rivron, Neil Innes and Phill Jupitus. The Idiot Bastard Band perform original comedy songs as well as cover versions, and their shows often feature guest performers. The group have continued to perform following the death of Brint in 2011.
Edmondson appeared on the BBC One television series That's Britain! which was broadcast from 23 November-14 December 2011. In each episode his task was to report as an "insider" in how a region of Britain works.
On 27 August 2012, Edmondson and Saunders became grandparents when their daughter Ella gave birth to a baby boy, Fred. In 2014, Ella gave birth to another son, Albert. Ella gave birth to their first granddaughter Ivy in August 2016.
He played the role of Gordon in the 2013 Chichester Festival Theatre production of Neville's Island. In 2014 it was announced that he would reprise the role for the show's West End run.
When Rik Mayall died in June 2014, Edmondson was one of the pallbearers at Mayall's funeral.
In 2015, Edmondson voiced Stanley the Dachshund in adverts for health and life insurance company Vitality.
From 2 November to 3 December 2016 Edmondson starred in an adaptation of william Leith's bestseller Bits Of Me Are Falling Apart at the Soho Theatre, London.
From November 2017 into 2018, Edmondson played the character of Malvolio in the Royal Shakespeare Company's production of Shakespeare's Twelfth Night.
