Transport Secretary Philip Hammond cut the ribbon at the 1.1 mile (1.8km) tunnel, on the London-to-Portsmouth A3 road, allowing traffic to go through.
He said: "This is another one of the missing links in Britain's trunk road network now put in place.
"The cutting-edge road scheme has surpassed expectations."
Southbound traffic is using the tunnel first, with northbound traffic due to start using it in a few days.
After that, work will begin to return the old A3 to nature, reuniting the Devil's Punchbowl with Hindhead Common for the first time in almost 200 years.
Construction began on the twin-bore tunnel in January 2007.
It is one of the longest in England and is part of a four-mile bypass of the Surrey village of Hindhead.
Seven safe crossing points have been built over or under the new road, most of them specifically for pedestrians, cyclists and horse riders.
A major new junction has also been built at Hazel Grove, and access roads have been laid for the businesses and properties that used to turn directly on to the busy A3.
The tunnel, which will be used by an estimated 30,000 vehicles a day, runs under the bowl which is a large hollow of dry, sandy heath, to the east of Hindhead.
The Highways Agency said its safety features include the UK's first radar-based incident detection system and 100% CCTV coverage.
The project has won awards for its innovation and its safety record, and has been delivered within budget and on schedule.
Mr Hammond said traffic had been held up at the Hindhead crossroads for years, "hampering the flow of goods and services and blighting the lives of people living in and around Hindhead".
"No longer. This new road will transform journeys on the A3 - improving journey times by around 20 minutes or more at busy periods - and will deliver a threefold return on investment for the economy," he said.
"This cutting-edge road scheme has surpassed expectations in almost every way, and sets a new standard for how vital infrastructure improvements can be delivered in a way that not only protects, but actually enhances the surrounding environment."
Thousands of motorists are expected to use the tunnel this week en route to the Glorious Goodwood race meeting in West Sussex.
The £371m Hindhead Tunnel under the Devil's Punch Bowl in Surrey has been officially opened after a four-and-a-half year construction project.