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 25-year-old had been with Silkmen since 2013 after starting his career at Stockport County.
He was captain of the Macclesfield side that lost at Wembley in the FA Trophy final this season to York City.
Halls is Chester's third close-season signing, after the arrival of strikers Harry White and Nyal Bell.
White was signed from Solihull Moors, while Nyal Bell has joined on a half-season loan from Gateshead until 7 January.
Jon McCarthy's side finished 19th in the table, narrowly avoiding relegation, having been seventh at Christmas.
Find all the latest football transfers on our dedicated page.

Ambulances and firefighters were called to the scene after a smell of smoke was reported shortly after 15:30 BST.
A generator that was inside a marquee has been turned off.
A spokesman for the Northern Ireland Ambulance Service said up to 40 people were being checked but no-one appeared to have become seriously ill.
"Nobody has been taken to hospital yet and we're not sure that anyone actually will [need] to be taken to hospital," John McPoland added.
He said firefighters called for ambulance staff at about 16:00 BST after a number of people at the circus complained of feeling unwell.
"We responded with three rapid response paramedics, one of our HART (Hazard Area Response) teams, two A&E crews and a patient care vehicle.
"The first paramedic on the scene gave us a situation report that no-body seemed too seriously ill as a result of the incident, and he just wanted further personnel there to help him check everybody out," Mr McPoland said.
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.
[NEXT_CONCEPT]
Chester have signed full-back Andy Halls on a one-year deal after he turned down a new contract with fellow National League side Macclesfield Town.
[NEXT_CONCEPT]
Paramedics have treated a number of people for the effects of breathing in fumes at a circus in Carrickfergus, County Antrim.