In a fresh ballot, 80.2% of members at the privately owned Scottish golf club, founded in 1744, opted to accept female members, overturning a previous vote held less than 12 months ago.
The R&A, the organizer of the Open Championship, moved quickly to reinstate Muirfield on the Open rota after it was removed in 2016.
The result of last May's vote caused a storm, with Scotland's First Minister Nicola Sturgeon calling the decision "indefensible."
Responding to Tuesday's announcement, Sturgeon tweeted: "Well done, Muirfield -- decision to admit women members emphatic and the right one. Look forward to seeing you host the Open again in future."
Women face a two-year wait
With a two-thirds majority needed to overturn the club's male-only stance, club captain Henry Fairweather said 498 votes had been returned in favor of admitting women, with 123 votes against.
The turnout was reported to be 92.7%.
"We look forward to welcoming women as members who will enjoy, and benefit, from the great traditions and friendly spirit of this remarkable club," said Fairweather.
Muirfield, home to the Honourable Company of Edinburgh Golfers, hosted the last of its 16 Open Championships in 2013, when America's Phil Mickelson lifted the famous Claret Jug.
Martin Slumbers, chief executive of the R&A, said: "It is extremely important for us in staging one of the world's great sporting events that women can become members of all our host clubs.
"Muirfield is a truly outstanding Open venue and we very much look forward to taking the Championship back there in future."
Previously, women had been able to play on the links course and visit the clubhouse as guests and visitors.
The club admits it is likely to take at least two years before the first woman joins the club.
"The current waiting list for membership at Muirfield suggests that new candidates for membership, women and men, can expect to wait two to three years, or longer, to become a member of the club," said a statement.