Scottish ministers gave the 28-mile road the go-ahead in 2009, but campaigners have been opposing the plans throughout an ongoing legal battle.
A two-day hearing at the court in London was held earlier this year.
Lord Reed delivered the judgement this morning, which looks to be a definitive decision on the £450m project.
Campaign group Road Sense's spokesman William Walton has conceded that the news today offers the opposition few options.
The decision was welcomed by Aberdeen Council leader Barney Crockett.
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"Today's announcement marks the end of a long, drawn-out and very frustrating process for the people and businesses of Aberdeen, the north east and indeed most of Scotland,” he said.
Aberdeenshire Council also hailed the news.
Leader Jim Gifford said: "It's the decision that we've all been waiting for and I'm delighted that after a decade of planning, enquiries and legal proceedings, we finally have the green light to move ahead with this project.
"Today marks the beginning of the delivery of the most significant piece of major infrastructure in the north east of Scotland since the discovery of oil in the North Sea in the 1960s."
The Scottish Building Federation welcomed the decision.
Chief Executive Michael Levack said: "Not only will this £450m project offer major opportunities during the construction phase, it also unlocks the future development of Aberdeen and Aberdeenshire for years to come.
"It will help the north-east to reach its full potential by enabling delivery of the new housing and other infrastructure the local economy needs to be able to grow. It sends a powerful message that this area of Scotland is open for business."
(IT)
