The deal, which replaces a previous decade-long agreement, is worth £13.0 billion ($20.3 billion) at current gas prices.
Centrica also unveiled a cash deal to buy North Sea assets run by Statoil for £1.0 billion, boosting the British group's oil and gas output by 25 percent.
Centrica and Statoil additionally signed a memorandum of understanding to consider working together on gas-focused exploration opportunities in Norway and Britain, according to a joint statement.
Under the supply agreement hailed by Prime Minister David Cameron as a deal that would help to protect Britain's energy security, Centrica will feed the country with 50 billion cubic metres of gas in the ten years to 2025.
"Today's agreement will help to ensure the continued security and competitiveness of gas supplies to Britain, from a trusted and reliable neighbour," Cameron said in the statement issued by Centrica.
The deal will provide enough gas to meet about five percent of Britain's total annual demand, or to supply 3.5 million homes.
Statoil president Helge Lund said the supply deal "demonstrates that natural gas is set to play an important role in the UK's long term energy mix.
"Natural gas has all the features needed for the UK to reach its long term energy policy goals of affordability, security of supply and CO2 emissions reduction," he noted.
Centrica, which owns British Gas, added that the main producing asset it was acquiring from Statoil was Kvitebjørn, which is located 170 kilometres northwest of Stavanger.
"The transaction increases Centrica's production by 34,000 barrels of oil equivalent per day, an increase of around 25 percent," Centrica said in the statement.
"Centrica also becomes an operator of producing assets in Norway for the first time," it added.
Centrica chief executive Sam Laidlaw said the asset deal "is an important further step in building the business and deploys capital to deliver value.
"Much of the gas acquired through this transaction will also come to the UK market, providing further energy security for British Gas customers long into the future," he said.