"A commercial agreement has been found with FOM (Formula One Management)," Pirelli motorsport head Paul Hembery told reporters.
"There is still the formal process to go through for final ratification at the FIA (International Automobile Federation) world council but we've been approved technically by the FIA," he added.
"We've got a bit of contract writing to do now, that will keep the lawyers busy for a little while, and then four years in front of us."
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Formula One's commercial supremo Bernie Ecclestone had earlier shaken hands with Pirelli chief executive Marco Tronchetti Provera on the Sochi starting grid and announced "we've done a deal."
Pirelli, the existing supplier, were competing against French company Michelin for the contract.
The technical rules and tyres are due to change significantly in 2017, with different widths front and rear, and Hembery said there would be a lot of testing needed before then.
"There is a recognition that we have to do high-quality testing to be able to deliver what the sport is asking for," he added.
"The solutions to the testing are obviously quite complex because the rules haven't been set yet. The question is can you test on a current car, or a modified current car or does it need a bespoke car?
"There are plenty of question marks (about) the practicalities of how we go testing but that will happen and we are going to be delighted to stay with the sport."
(Editing by Ed Osmond)
