In 1979, Daniel Brélaz became the first green representative elected to sit in a national parliament.
Brélaz received a degree in mathematics from École polytechnique fédérale de Lausanne (EPFL) in 1975, and afterwards taught mathematics. He is responsible for a well-known approximation algorithm for graph colouring.
In 1975, he joined the Group for the Protection of the Environment in Lausanne. In 1978 he was one of the first environmentalists elected to parliament, in the Grand Council of Vaud, and re-elected in 1982-83.
From 1979 to 1989, Brélaz was the first environmentalist elected to sit in a national parliament, in the National Council of Switzerland.
In 1989, he was elected to the City Council of Lausanne where he was responsible for industrial services. On 25 November 2001, he became the trustee responsible for finance, and was re-elected in the first round of Vaud elections on 12 March 2006.
In 2007, he was elected again to the National Council. He resigned his seat on the Grand Council of Vaud but remained a trustee in Lausanne, and was criticized for maintaining this dual mandate.
On 13 March 2011, he was re-elected in the first round of the Lausanne municipal elections with 11,503 votes in his favour.
Daniel Brélaz is vice-president of the Administrative Council for Public Transportation in the Region of Lausanne.