Wigglesworth is a native of Sussex, England. He studied conducting at the Royal Academy of Music in London and won the Kondrashin Conducting Competition in Amsterdam in 1989. He has since served as associate conductor of the BBC Symphony Orchestra, music director of the BBC National Orchestra of Wales, and principal guest conductor of the Swedish Radio Symphony Orchestra.

Wigglesworth is an active opera conductor, having led performances at the Welsh National Opera, Covent Garden, the Metropolitan Opera, the English National Opera, and Glyndebourne.

He has worked with North American orchestras including the New York Philharmonic, Chicago Symphony, Los Angeles Philharmonic, San Francisco Symphony, Philadelphia Orchestra, Montreal Symphony, and Toronto Symphony. He regularly conducts the Cleveland Orchestra, the Minnesota and Detroit Symphony orchestras.

In Europe, Wigglesworth has led orchestras including the Berlin Philharmonic, London Philharmonic, London Symphony Orchestra, Royal Concertgebouw Orchestra, and Rotterdam Philharmonic Orchestra.

He works closely with the Netherlands Radio Philharmonic Orchestra, with whom he is currently recording a Shostakovich symphony cycle for BIS records.