Hume was born in Peebles but raised in Selkirkshire and currently lives on a farm in the valley of the Yarrow Water. His previous positions include Chairman of "Environment and Land Use" for the National Farmers Union of Scotland and President of Lothians and Borders NFU. He was active during the Foot-and-mouth crisis of 2001. Before becoming an MSP, he was also on the board of Scottish Enterprise Borders, Chaired The Borders Foundation for Rural Sustainability and was a Trustee of The Borders Forest Trust.
He was elected to the Scottish Parliament to represent the South of Scotland region at the 2007 election. He was also elected councillor of the Galashiels and District region of Scottish Borders Council on the same night. He is the first ever Liberal Democrat MSP for the South of Scotland region since the Scottish Parliament was created in 1999. Hume is currently Scottish Liberal Democrat Spokesman for Housing and Health. He sits on the Scottish Parliament's Rural Affairs, Climate Change and Environment Committee, of which he is the Committee's EU Reporter. He is also the Scottish Liberal Democrat Deputy Whip and is also a member of the European Committee of Regions.