The club's 2,400 worldwide members voted in person and via proxy and postal votes, and, after being encouraged by chief executive Peter Dawson and the club's committees, more than 75 percent took part with 85 percent in favour of the change.
"This is a very important and positive day in the history of the Royal and Ancient Golf Club," Dawson said in statement.
"The R&A has served the sport of golf well for 260 years and I am confident that the club will continue to do so in future with the support of all its members, both women and men."
Founded in 1754, the Royal and Ancient's members play on the St Andrews links course regarded as the "home of golf".
Although women have been allowed to play on the course, they were, until Thursday's vote, not allowed in the clubhouse and had no significant part in the sport's rulemaking arm, the R&A.
That body, separated from the club 10 years ago, controls golf around the world apart from in the United States and Mexico.
Helen Grant, Britain's minister for sport, welcomed the move.
"I am pleased that the members of the Royal and Ancient Golf Club have voted in favour of admitting women members," she said,
"This is positive news for the sport and I hope we will now see other golf clubs that still have outdated same sex policies follow suit.
"With golf in the next Olympics there is a huge opportunity for the sport to grow and this sends out the right inclusive message that golf is for everyone."
The announcement was also welcomed by Ted Bishop, president of the PGA of America.
"Women have played and will continue to play an integral role in the game of golf. In fact, women represent the biggest growth market in the sport, and every step to make golf more inclusive is good for the game," he said in a statement.
"The PGA of America is thrilled that the R&A is welcoming women into its organisation, and loudly applauds its decision."
(Editing by Ed Osmond)
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