After his studies at the "Hoger Rijksinstituut voor Toerisme, Hotelwezen en Voedingsbedrijven", Stevaert started as a bar owner in 1972. He became politically active in 1982 under the wings of his mentor Willy Claes. Stevaert was elected to the Provincial Council of Limburg from 1985 to 1995.
He became mayor and member of the city council of Hasselt in 1995. There he became famous for his policy of free public transport in 1997, which gave him his nickname "Steve Stunt". Stevaert was in 1995 also elected to the Flemish parliament and was re-elected in 1999 and 2004.
Stevaert served as Flemish minister of Public Works, Transport and Spatial planning from 1998 to 1999 and as Flemish minister of Mobility, Transport and Public Works from 1999 to 2003, when he resigned having become chairman of his party, succeeding Patrick Janssens.
He was chairman from 2003 until he resigned on May 25 2005, having been appointed governor of the province Limburg, in which function he succeeded governor Hilde Houben-Bertrand. He became the 15th governor, and also the first 'socialist' governor of this province. Caroline Gennez succeeded him as temporary chairman, until Johan Vande Lanotte became officially elected as the new chairman in October 2005.