The singer, songwriter and guitarist died shortly after walking his dog.
The private service was held at West London Crematorium, attended by Joe Strummer‘s widow Lucinda, two daughters and a step-daughter.
It is believed that former Clash bandmates Mick Jones, Paul Simonon and Topper Headon joined family and friends at the service.
The funeral cortege passed what used to be The Elgin pub in Ladbroke Grove, where Clash played some of their earliest gigs 25 years ago.
Mourners have been asked not to send flowers but instead to donate funds to an Aids charity concert in South Africa that Joe Strummer was due to attend in February.
See next week’s NME (out 8 January) for a full Joe Strummer obituary and tributes.