His musical career began with a bachelor's degree with honours from University of Winnipeg in 1986.

Demos of Roberts's songs found themselves in the hands of various music company execs across Canada, and the quirky bar band that had just begun to write original material found itself with record deal options which led The Crash Test Dummies into a rushed, but nevertheless well-received debut album, The Ghosts that Haunt Me. The album introduced the band to the rest of the Canadian provinces, selling over 400,000 copies in Canada alone and also garnering a 1991 Juno Award for Group of the Year.

With more time and finances, Roberts set about writing the band's second album, God Shuffled His Feet. This to date is the band's best selling and most popular album, taking them into the international arena of musical exposure. The album has sold over six million copies and caused The Crash Test Dummies to be nominated for three Grammy Awards in 1994. The group was nominated for eleven other Junos from 1992 to 2000.

A Worm's Life was released in 1996, selling over one million copies and showcasing a harder-edged sound as the band continued to evolve, producing this album on their own.

1999 introduced a mix of electronic funk and spontaneous wordplay with Give Yourself a Hand. Roberts met Greg Wells at a songwriters' workshop and invited him to co-write and assist in recording this album inspired by influences and flavours of Roberts' new home in Harlem, New York.

On September 28, 2000, Roberts was severely injured when he crashed his car on a dirt road in Yarmouth County, Nova Scotia. Marijuana was discovered in his pocket while he was loaded into an ambulance and he was then charged for possession by the RCMP. While he was recuperating from the accident, he began jamming with locals (The Great Wind Jammers from Argyle, Yarmouth County) and produced from these sessions I Don't Care That You Don't Mind. This was the first album released by the band independent of a major record label.

Puss 'n' Boots was released in October 2003 with a European and additional American version.

Roberts married Michele Varian of Detroit, Michigan in 2004. Roberts and his wife now live in SoHo, New York, where he continues to write and record his music. He has had many artistic opportunities to work with other artists such as Joe Jackson, Scotty Hard, Greg Wells, Deltron 3030, and Medeski Martin & Wood.

A new Crash Test Dummies album, Oooh La La!, was released in 2010. This was followed with the solo release on an album of Mantras, entitled Rajanaka: Mantra, in 2011.