Members at the East Lothian club decided by a ratio of four to one to admit women 10 months after a first vote failed to achieve the two-thirds majority required, a decision which saw it struck off the list of Open venues.
The R&A responded almost immediately to the second vote, but change to the make-up of the Honourable Company of Edinburgh Golfers will not happen as quickly.
The 273-year-old group, which owns and runs the course, estimates it will be “two to three years, or longer” before the first woman completes its admissions procedure.
Captain Henry Fairweather announced the rule change had been passed by 498 votes to 123 on a turnout of more than 90 per cent.
Moments later the R&A released a statement which stated Muirfield’s history of staging the Open - it has done so 16 times - would continue, although the earliest that can next happen is 2022.
Chief executive Martin Slumbers said: “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.
"Muirfield is a truly outstanding Open venue and we very much look forward to taking the Championship back there in future.”
Past Muirfield champions include Gary Player, Jack Nicklaus, Lee Trevino, Tom Watson, Nick Faldo, Ernie Els, and Phil Mickelson.
Fairweather said: “The Open was a great event in 2013 here. It was much enjoyed by the members and we have had a very long, historical association with the Open and we would very much like to see it back here at Muirfield.
“After the 2013 Open a study suggested it was worth about £70m to the local economy and I know that’s very important to East Lothian Council and the business community.”
Fairweather revealed the idea of fast-tracking women onto the membership was not on the agenda.
“Our members were quite clear that they wanted women to be treated, not in any artificial way, but to go through the same admissions process as men,” he said.
“That means it will take a little time for women to become members. We’ve got quite a complicated admissions process and we have a waiting list.
"They don’t apply, they have to be proposed and seconded by members, but anybody who is interested in becoming a member of Muirfield, I would say: ‘Go for it.”’
Fairweather stated that the process of persuading reluctant members had begun soon after the first vote.
“I think the main assurance that people were looking for was the essential character of our club will not be fundamentally changed by the introduction of women members, that foursomes match-play golf will remain our staple diet here, that rounds of golf will take less than three hours to complete and we will enjoy each other’s company,” he said.
But the engagement failed to convince one in five members.
“I think that’s a challenge for future committees but I have great confidence that, as time evolves, people will find their concerns are not borne out,” Fairweather said.
He admitted criticism of the club last year had made things “uncomfortable” but was keen to stress the committee’s engagement with the community in Gullane and beyond.
“I think people have understood the club has come a long way in quite a short space of time, and certainly I think quite a lot of people were encouraged by the fact we quite quickly announced we were intending to have a second vote,” Fairweather said.
“That reassured people. We have been put under no pressure from the local community.”
The decision was widely welcomed. Scotland’s First Minister, Nicola Sturgeon, had labelled the first vote “simply indefensible”.
Writing on Twitter after the U-turn, she said: “Well done, Muirfield — decision to admit women members emphatic & the right one. Look forward to seeing you host the Open again in future.”
Ladies European Tour chief executive Ivan Khodabakhs said the decision would “begin to restore the reputation of the club”.
Former Women’s British Open winner Catriona Matthew, who lives about five miles along the coast in North Berwick, wrote on Twitter it was great news and gave “kudos” to the R&A for reinstating Muirfield to Open rota.