Transport Secretary Grant Shapps granted permission on Thursday for the works — which include a two-mile tunnel — to go ahead.
They also fear the works could destroy any areas of potential archeological significance.
The decision means Highways England, which first submitted a planning application in 2018, has the green light to make changes to the major single carriageway A303 road, which famously runs close alongside the monument and is regularly beset by traffic jams.
Highways England welcomed the decision and said the project will reduce the sound of traffic.
Site preparations for the dual carriageway will begin next year, Highways England added.
But the government’s decision is controversial because the examining body for national planning applications, the Planning Inspectorate, had recommended that the government “withhold consent.”
Stonehenge is famous because there remains much mystery around why the monument was constructed, and how the gigantic stones that form the structure were transported.
Campaigning group Stonehenge Alliance, which has fought against the tunnel’s construction, has also said the “road widening” would damage parts of the surrounding area.
The single carriageway A303 road is very close to the neolithic stone monument. Campaigners say they are against the road being widened.
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Environmental campaigning group Greenpeace was also critical of the government’s decision.
Richard George, head of transport at Greenpeace UK, said in a statement Thursday that the tunnel would be a “disaster for England’s heritage and the world’s climate.”
“If the government is serious about a green recovery from the pandemic it should be investing in public transport, but instead we’re getting more traffic and more pollution,” George said.
But the move was welcomed by English Heritage, which manages the prehistoric site.
A spokeswoman for English Heritage told CNN in a statement that replacing the “busy” A303 with a tunnel would “transform Stonehenge, reunite the landscape and allow people to not only better enjoy and understand the ancient stones but to explore the surrounding countryside and discover its many other fascinating prehistoric monuments.”