Scientists say the probe's instruments indicate it has moved beyond the bubble of hot gas from our Sun and is now moving in the space between the stars.
Launched in 1977, Voyager was sent initially to study the outer planets, but then just kept on going.
This distance is so vast that it takes 17 hours now for a radio signal sent from Voyager to reach receivers here on Earth.
"This is really a key milestone that we'd been hoping we would reach when we started this project over 40 years ago - that we would get a spacecraft into interstellar space," said Prof Ed Stone, the chief scientist on the venture.
"Scientifically it's a major milestone, but also historically - this is one of those journeys of exploration like circumnavigating the globe for the first time or having a footprint on the Moon for the first time. This is the first time we've begun to explore the space between the stars," he told BBC News.
Sensors on Voyager had been indicating for some time that its local environment had changed.
The data that finally convinced the mission team to call the jump to interstellar space came from the probe's Plasma Wave Science (PWS) instrument. This can measure the density of charged particles in Voyager's vicinity.
Readings taken in April/May this year and October/November last year revealed a near-100-fold jump in the number of protons occupying every cubic metre of space.
Scientists have long theorised such a spike would eventually be observed if Voyager could get beyond the influence of the magnetic fields and particle wind that billow from the surface of the Sun.
When the Voyager team put the new data together with information from the other instruments onboard, they calculated the moment of escape to have occurred on or about 25 August, 2012.
- India Violet Updated at: Saturday, September 14, 2013