The decision by Kent County Council paves the way for the first major expansion of a grammar school in England for half a century.
Members of the council overwhelmingly backed a 2,600-plus name petition demanding a boost in grammar school places in Sevenoaks to meet high demand.
Under Government legislation, it is not possible to set up a new selective school but a relaxation of rules last year allows existing schools to open an annexe to cater for strong demand for places.
The vote in Kent will allow the building of two separate annexes to a male and female grammar school in Tonbridge and Tunbridge Wells as part of satellite facilities.
However critics have accused the coalition government of "sneaky" changes, with the shadow education secretary Stephen Twigg claiming in January that selection at age 11 was being expanded through the "back door".
Some campaigners have warned that some institutions could be effectively killed off as nearby grammars grow and attract the brightest pupils.
But the Department for Education (DfE) said the over-riding objective of thereforms was to increase the supply of good school places, whether they were selective or otherwise.
This afternoon, 66 councillors voted in favour, three opposed and one abstained on a vote on the changes following an hour-long meeting at County Hall in Maidstone.
Campaigner Andrew Shilling told the meeting that not having a grammar school in Sevenoaks was an "injustice" and had a "profoundly negative effect" on local children.
He said the long distances they have to travel was having a negative effect on their learning, and their opportunities for hobbies and to develop friendships.
He told councillors: "Many of us present, including me, benefited from the excellent education that Kent grammar schools provide. Unfortunately, Sevenoaks is the only major town within the Kent grammar school system that is without a grammar school."
Expansion of selective education on a new satellite site has not happened since the 1960s, although Torquay Boys' Grammar School in Devon started talks last year to set one up seven miles away.
Supporting the campaign, KCC leader Paul Carter said: "It's time we did make a significant investment in the proportionate expansion of selective schools in west Kent.
"The existing grammar schools in Tunbridge Wells and Tonbridge are working at their physical capacity."