The new technical, sporting and financial rules include a budget cap and represent the fruit of two years of discussions between teams, governing body and U.S.-based commercial rights holders Liberty Media and other stakeholders.
They were earlier approved unanimously by the governing FIA's World Motor Sport Council, with talks continuing over governance and profit sharing.
"The goal has always been to improve the competition and action on the track and at the same time make the sport a healthier and attractive business for all," said Formula One chairman Chase Carey.
"The approval of the rules by the World Motorsport Council is a watershed moment and will help deliver more exciting wheel to wheel racing for all our fans."
The heavier 2021 cars are the products of a changed aerodynamic approach, with simpler front wings and bigger wheels.
The budget cap has been set at $175 million for each team, about half what some of the top outfits like Mercedes, Ferrari or Red Bull spend at present but still much more than some others can muster.
Formula One's managing director for motorsport Ross Brawn recognised the new cars would be slower than the 2019 ones, but still quick and closer to the levels of performance seen in 2016 as well as easier to follow and overtake.
Both Mercedes and Ferrari are going to have to reduce their spending in the future
Image credit: Getty Images
FIA president Jean Todt said the 2021 regulations represented a "truly collaborative effort" and added that environmental considerations were a crucial element for the governing body.
From 2021, the aim is to double the renewable content of fuel to 20%.
"Formula One already has the most efficient engines in the world, and we will continue to work on new technologies and fuels to push these boundaries further," said Todt.