Brelaz was elected to the National Council, the lower house of Switzerland's Federal Assembly, in 1979.
He died following a heart attack, his son told Switzerland's domestic Keystone-ATS news agency.
Brelaz, upon his retirement in 2022, told Swiss national broadcaster that "I am proud because I got it right" regarding environmental consciousness in politics.
"I entered the National Council (parliament) with new concerns such as sustainable economics and recycling, not just renewable energy. Forty years later, these concerns have shaped the future of the country's politics."
Born in 1950, Brelaz graduated in mathematics from Lausanne's EPFL university in 1975 and became a teacher.
After joining environmental politics in a campaign against the construction of a nuclear power plant, he was elected to the Vaud cantonal legislature in the French-speaking western region in 1978.
Brelaz then stood for parliament, and was elected aged 29. He was still living with his parents at the time.
He served three spells in the National Council: from 1979 to 1989, from 2007 to 2011, and finally from 2015 to 2022, retiring before the end of his term following a domestic fall.
The Green Party is currently the fifth-largest in the 200-member National Council with 23 seats, followed by the Green Liberal Party with 11.
In 2001, Brelaz became the first directly-elected Green mayor in Switzerland, spending 15 years as mayor of Lausanne, the country's fifth-biggest city.
"Daniel Brelaz was, a remarkable figure in every respect, thanks to his stature, his keen intelligence, and his mental arithmetic skills," the Vaud cantonal executive said in a statement.
His family said a memorial service would be held at Lausanne Cathedral at a date to be arranged.
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