Moss was born in Clapham Jewish Boys Home at Wandsworth, South London, and was adopted when six months old by Rosetta (née Goldsmith, b. 1929) and Lionel Moss (b. 1927, d. 1999), an upper-middle-class couple of Jewish ancestry. His father owned a clothing store called Alkit, located at Cambridge Circus. He grew up in Hampstead, attending Arnold House School (1962–1970) and Highgate School (1970–1975).
During Moss's childhood, music began to have an important role in his life, and he would play well-known songs on his family's piano. His elder brother, David, was drummer in a school band and had a Wayward drum kit, which Jon borrowed to start playing when thirteen years old.
At Highgate School, Moss developed a fascination for sports, especially boxing, but he did not want a professional sporting career. It was also at Highgate that he formed his first band, Pig Williams, along with his friend Nick Feldman (who would later become a member and co-founder of Wang Chung). Together they performed at several school events. After finishing high school, Jon held various jobs, including working at his father's clothing store, as a cake salesman and as a sound engineer at Marquee Studios. In spite of regarding a college graduation as a waste of time, he briefly considered the idea of studying Greek at the University of Cambridge.
Alongside his friend Riff Regan, Moss joined the punk band London in 1976, after being tried out as a drummer with The Clash; later, he said "The mix of personalities didn't work. Their attitudes were too different to mine." London released a single entitled "Everyone's a Winner", and were managed by Simon Napier-Bell. Eventually they recorded two singles, a four-track EP and an album for MCA Records in 1977. Following this, Moss went on tour with established punk group The Stranglers, and the band got a record deal.
Soon afterward, Moss began drumming with The Damned, replacing Rat Scabies who had quit the band. He made the final decision to join them, after he was injured in a car crash on New Year's Eve 1977, when he suffered fractures to his face (his injuries required 250 stitches), resulting in a broken nose and a week's hospital stay.
He played with Adam and the Ants, before their commercial success, on their third single "Cartrouble" and its b-side "Kick!". At the time Moss was with a group called Jane Aire & The Belvederes, and under contract with that band: therefore he was credited on the original single under the pseudonym "Terry 1 & 2".. He has since been credited under his real name on reissues of the tracks, starting with the 1984 CBS/Epic reissue of Dirk Wears White Sox.
Moss was advised by a friend that Boy George was looking for a drummer for his band. When he became a member of the band—which was originally called In Praise of Lemmings—he suggested changing the name of the group to Culture Club, in reference to the various ethnic backgrounds of the members.
In 1985, whilst still performing with Culture Club, he produced some tracks for the band Woyeyeh.
After Culture Club broke up in 1986, Moss released a single entitled "Jump To It" with the group Heartbeat UK, which he also produced.
In 1989, under the name Rubberman, Moss released one white label of an acid house instrumental track. Boy George used that backing track to create his own song "After The Love", which was released as a single by Jesus Loves You).
During 1991 and 1992 Moss was involved in another group, Promised Land, with his schoolfriend Nick Feldman. The two released two singles, "Something In The Air" and "Circle In The Square", and also a self-titled album.
In 1995 he met Sebastian Wocker, vocalist of the indie band Yeah, and soon joined them. For two years the group played several concerts on the London circuit, made various television appearances and filmed one video Engerland in 1997 at the former home of Hendon F.C.. Their last concert was at The Underworld in Camden Town in 1998.
Moss was a part of the Culture Club reformation between 1998 and 2002.
From 2003 to 2005 Moss joined several punk rock and rock bands, among them Fassbender, DanMingo and Dirth. In July 2005 he played drums on the charity single "People I Don't Know Are Trying to Kill Me", written by the journalist Neil McCormick, to help the families of the victims of the terrorist bombings in London. He has also performed and recorded with the London-based singer and songwriter Anca.
In 2006 Moss, Mikey Craig and Phil Pickett tried to launch Culture Club on a new tour with another lead singer, as George and Roy Hay had declined to tour. An UK tour was announced for December 2006, but was postponed to give the new line-up time to finish recording their album. Without official press statements, band manager Tony Gordon said in 2007 that the project was "on hold", while Jon stated that the project was shelved.
Moss was interviewed in May 2009 by the Hampstead Village Voice about his early life and career.
In 2010 he also played a few gigs with the band Plastic Heroes.
Jon Moss is involved with the reunion of Culture Club, which was rumoured to include a new album and a world tour. However he did not appear at the band's concerts in Dubai and Sydney in December 2011, due to a back injury which required surgery. Despite rumours that the reunion project had been shelved, Boy George said in an interview with Danny Baker on BBC Radio 5—which aired in March 2012—that their new album would be released in 2013, but did not mention any date for a tour.
Meanwhile, Moss had been drumming with Mad Dog Bites, alongside Martin French (vocals), Godfrey Old (harmonica), Peter Noone (bass) and Conrad Blakemore (guitar). Bob Weston was their guitarist until his death in January 2012.
In the Red Nose Day '13 at Whiteleys, Moss sang with The Rock Choir, helping them to fundraise for Comic Relief.
Jon Moss has three children by his former wife Barbara Savage.
Moss had a relationship with Boy George during the height of Culture Club's popularity, although it was not public knowledge at the time. Their affair came to an end in 1986; it was portrayed in Worried About the Boy, a drama film shown on BBC2.