Club captain Henry Fairweather announced that the necessary two-thirds majority had been reached, with 80.2 percent of members voting in favour of change.
"We look forward to welcoming women as members who will enjoy, and benefit from, the great traditions and friendly spirit of this remarkable club," he said.
The R&A, the body that organises The Open, declared Muirfield back on its list of eligible courses, having said last year it would not stage the tournament at a venue that did not admit female members.
Muirfield has had a male-only membership policy since the Honourable Company of Edinburgh Golfers, which controls the course, was founded in 1744. Women are allowed to play there, but an initial ballot to allow women members failed in May last year when only 64 percent voted in favour.
That result drew criticism from several top golfers, including four-times major winner Rory McIlroy.
Scotland's First Minister Nicola Sturgeon, who had called the initial ballot "simply indefensible", took to Twitter on Tuesday to express her approval.
"Well done, Muirfield - decision to admit women members emphatic & the right one. Look forward to seeing you host the Open again in future," she said.
Martin Slumbers, chief executive of the R&A, agreed.
"Muirfield has a long and important history of hosting The Open and with today’s announcement that will continue... We very much look forward to taking the Championship back there in future," he said in a statement.
Muirfield has hosted the Open 16 times, most recently in 2013 when it was won by American Phil Mickelson.
The Royal St George's club in Kent was recently awarded hosting rights for the 2020 Open after it too voted to allow women members in 2015.
Britain's Sports Minister Tracey Crouch said on Twitter that Muirfield's decision "was a long time coming but endorses @RandA position that women contribute positively to golf."
The Ladies European Tour (LET) said the vote would "begin to restore the reputation of the club".
"Sports reflect the values of the society in which we live and today men and women have equal rights. We believe this should be reflected not only in top level international tournaments but also at club level," it added.
(Reporting by Alan Baldwin, editing by Mark Trevelyan)
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