Stevaert was born on 12 April 1954 in Rijkhoven in Belgium. After his studies at the "Hoger Rijksinstituut voor Toerisme, Hotelwezen en Voedingsbedrijven", Stevaert started as a bar owner in 1972.
Stevaert 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 also elected to the Flemish parliament in 1995 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 was officially elected as the new chairman in October 2005. On June 9, 2009, the day of the Flemish regional elections, Stevaert announced he would step down as governor. He was succeeded by his fellow socialist Herman Reynders.
In early April 2015 allegations of rape were made public in the Belgian media. Subsequently, on April 2, 2015, the public prosecutor of Hasselt confirmed that Stevaert had gone missing. Near 1800 hrs divers found his body in the Albert Canal near Hasselt.