Hill added: "It's not easy to enter into an agreement of this magnitude. It's a big commitment.
"But the BRDC felt we wanted this relationship to continue and we were prepared to back the negotiating team, with the level of risk satisfactory for the deal to go ahead."
F1 chief Bernie Ecclestone welcomed the deal, adding: "This will ensure the British Grand Prix is included on the Formula 1 calendar for many years to come, which is something I've always wanted.
"The team at Silverstone already know how to organise a good event and now everyone can look forward to next summer at Silverstone."
The 2010 race calendar will be officially released later this week, when the Silverstone showpiece will be confirmed for Sunday, 11 July - the same day as the 2010 World Cup final.
Talks had been ongoing between Formula 1 Management (FOM) and Silverstone since Donington Park failed to show it had the necessary £135m funding.
Button happy with Silverstone decision
The main delay in establishing a deal appears to have been the length of the contract and the inclusion of a 7% annual escalation fee.
Silverstone, which first staged the British Grand Prix in 1948, admitted it needed to improve its ageing facilities but insisted it required the security of a longer-term contract to justify and help raise the finances needed to upgrade.
The contract on the table was believed to demand a £12m fee for 2010, with an increase of 7% per year after that.
However, it is now understood the increase has been pegged at 5%.
There is also a clause in the contract that allows either side to end the contract after 10 years.
BBC F1 commentator, and former F1 driver, Martin Brundle said: "It's brilliant news. I always assumed it would happen in the end because everyone wanted the same thing. The new circuits are exciting and interesting but they always had to balance up with the historic circuits, like Silverstone."
Silverstone managing director Richard Phillips added: "We've always had five-year deals and never been able to get the investment we needed to redevelop.
Classic F1 - British Grand Prix 1987
"But 17 years gives us the ability to invest and move forward.
"We've always had the belief the British Grand Prix was an important cornerstone of Formula 1 but, with Bernie, you're never quite sure. At the end of the day, though, you have to have a British Grand Prix."
Sports minister Gerry Sutcliffe was quick to welcome the announcement and said: "The news the British Grand Prix is to stay at the iconic Northamptonshire track will be welcomed by millions of fans - not just in this country but across the world."
Silverstone is also set to stage the British MotoGP in 2010 on a modified track.
The revamped layout will also be used for the F1 race, as long as Silverstone officials can get approval from the FIA, the sport's world governing body. If not, they will stick with the old circuit.
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