The announcement ends the BBC having live rights for the world’s oldest major for close to 60 years, with it being left with only highlights.
“We believe this is the best result for The Open and for golf,” said the R&A’s chief executive Peter Dawson.
“The way people consume live sport is changing significantly and this new agreement ensures fans have a range of options for enjoying the Championship on television, on radio and through digital channels.
“Sky Sports has an excellent track record in covering golf across its platforms and has become the home of live golf coverage over recent years. “We are very much looking forward to working with them to develop and enhance the coverage of The Open.”
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Dawson, who also posted an open letter on the championship’s website, added: “We have enjoyed a long and successful relationship with the BBC and, although the nature of that relationship is changing from 2017, we are delighted that the BBC will broadcast prime-time highlights and that the Championship will continue to benefit from extensive live coverage on Radio 5 Live and online.
“Importantly, the new agreement will enable us to increase substantially our support for golf in the United Kingdom and Ireland.
“That our increased commitment to golf in both countries is to be supported by both Sky Sports and the BBC is a hugely positive step for our sport.”
While no figures were revealed, it is believed the new deal is worth £10m per year - £3m more than the current contract that only has this summer’s event at St Andrews and next year’s at Royal Troon left to run.