The Honourable Company of Edinburgh Golfers, which owns Muirfield and is the world's oldest golf club, held a second postal ballot after members voted last May to retain the male-only policy. That led to Muirfield being taken off the British Open rotation.
The results of the second vote were announced Tuesday outside Muirfield's clubhouse, with club captain Henry Fairweather saying that 80.2 percent of those who voted chose to allow women to become members. A two-thirds majority was required for change.
A total of 621 members voted, a turnout of 92.7 percent.
The R&A, which organizes the British Open, said minutes after the announcement that Muirfield was back in the rotation to stage the world's oldest major.
''It is extremely important for us in staging one of the world's great sporting events that women can become members at all of our host clubs,'' the R&A said. ''Muirfield is a truly outstanding Open venue and we very much look forward to taking the championship back there in future.''
Muirfield has staged the British Open 16 times since 1892, most recently in 2013 when Phil Mickelson won.
''This is a significant decision for a club which was founded in 1744 and retains many of the values and aspirations of its founding members,'' Fairweather said. ''We look forward to welcoming women as members who will enjoy, and benefit from, the great traditions and friendly spirit of this remarkable club.''
The club's original decision to retain its male-only policy provoked sharp criticism from players and lawmakers, who said that golf was failing to mirror modern society. Scottish First Minister Nicola Sturgeon had said it was ''simply indefensible.''
''Well done Muirfield,'' she posted on Twitter after the results of the second ballot were announced. ''Decision to admit women members emphatic and the right one.''
Scotland's minister for sport, Aileen Campbell, said the decision was ''extremely positive for equality in Scotland.''
''Scotland is a modern country that wants to see gender equality become the norm across all parts of society,'' Campbell said, ''and today's decision is another step forward in that journey.''
The Royal and Ancient Golf Club at St. Andrews opened its membership to women in 2014 for the first time in 260 years. Royal St. George's and Royal Troon, two other British Open hosts, ended their male-only membership policies last year. Augusta National, home of the Masters, decided in 2012 to invite women to join.
The HCEG said new candidates for membership, both men and women, can expect to wait ''two to three years, or longer,'' to become a member of Muirfield because of the current waiting list.
Females were previously allowed on the course and in the clubhouse at Muirfield as guests and visitors only.
The host courses of the British Open have been announced through 2021.
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