The men's British Open is played on links, or coastal, courses.
But Sunningdale, about 25 miles (40 km) southwest of London, is an inland course.
"We know Sunningdale will provide an outstanding venue in two years," said R&A chief executive Mark Darbon.
"It will be the fifth time the championship has been held there and the first since 2008."
Royal St George's in Kent is set to host the 2027 Women's British Open.
The R&A has increased the official prize fund for this year's tournament at Royal Lytham & St Annes to £7.4 million.