Exelby studied for a politics degree at Durham University and became editor of Palatinate. After leaving university he worked at The Northern Echo newspaper before joining BBC Television news where he was news editor, editor of most of the major news programmes and co-founder and managing editor of BBC World TV News. He is married to Judith Hann who was formerly a presenter of Tomorrow's World for 20 years. They both run a media company based in the Cotswolds.
He died on 15 November 2019 at the age of 78.