He was born in Edinburgh, Scotland, and brought up in Cupar, Fife where he went to Bell Baxter High School. After studying mathematics at the University of Aberdeen he worked in information technology with Bank of Scotland for 30 years retiring in 1999 as Director of Technology Innovation.
He joined the Scottish National Party (SNP) in 1961. Elected to the Scottish Parliament on 7 June 2001 he followed Alex Salmond, after his resignation, as member of the Scottish Parliament (MSP) for Banff and Buchan.
In 2004 he was a member of the Scottish Parliament team in the TV general knowledge program, University Challenge - The Professionals. He and fellow team members Richard Baker (Labour), Robin Harper (Green), Jamie Stone (Lib Dem) who was captain, beat a Welsh Assembly team by 110 points to 75. Both teams comfortably surpassed the record low score of 25 achieved by the House of Commons team in 2003
In opposition he was Shadow Deputy Justice Minister with responsibility for Prisons and Drugs policy, Convenor of the SNP Group in the Scottish Parliament and Deputy Convenor of the Parliament's Justice 1 Committee. In addition he ended Session 2 as a substitute member of the Parliament's Health Committee and Deputy Convenor of the Parliament's Cross Party Group on Visual Impairment.
He can, arguably, hold the record for the longest speech in Parliament. He commenced a speech on International Suicide Prevention Week at 17:21 on Wednesday, 7 September 2004 and completed it at 17:12 on Thursday, 8 September 2004 nearly 24 hours later. However this was due to the failure of the Parliament's sound system just after he started to speak.
In the Scottish Parliament election of 3 May 2007, Stewart Stevenson was returned with a majority of 10,530, the largest in Scotland, over the Scottish Conservative Party candidate. After the SNP's victory at the 2007 Scottish Parliament Election, Stevenson was appointed Minister for Transport, Infrastructure and Climate Change. This appointment covers: the land use planning system, climate change, building standards, transport policy and delivery, public transport, road, rail services, canals, harbours, air and ferry services, Scottish Water.
As Minister, Stevenson piloted the SNP's first Bill, Abolition of Bridge Tolls (Scotland) Bill, to the statute book on 24 January 2008.. He also brought forward the SNP's first Legislative Consent Motion, previously known as Sewel Motions, on the subject of the UK Climate Change Bill. He was also the first SNP Minister to lose a vote in Parliament on the subject of the Edinburgh Trams project.
He continues a family association as the Minister for Transport through the planning and building of the replacement for the Forth Road Bridge which opened in 1964. His great uncle Sir Alexander Stevenson was Chairman of the Forth Road Bridge Campaign Committee in the 1930s.