Stewart was born in Dundee in 1963. He was educated at Brackens PS, Invertay PS Monifieth, Carnoustie High School, and Bell Street Tech (now Abertay University) where he gained an HD in Computer Studies.
 
Stewart is a highly experienced political campaigner, Stewart was the SNP's first Youth Convener and spent four years as the Party's National Secretary before being elected as the Organisation Convener in 2003.

Stewart contested the Dundee East Westminster seat in 2001 delivering a 5% swing to the SNP and slashing the Labour majority by 5,500 votes. He won the seat in 2005, held it in 2010, again in 2015 and in 2017 was returned with the largest majority of any SNP MP. In 2019 he was elected for a fifth time with an increased majority of 13,375.