The rule change required a two-thirds majority from members
Muirfield has voted to allow female members after over 80% of the membership agreed to the rule change.
The Scottish course had been removed from the rota to host the British Open after The R&A announced all host courses had to allow female members.
The Edinburgh course previously voted on the issue in 2016 but fell just short of the two-thirds required with a 64% vote in favour of the change back then.
The R&A released a statement commending the vote and confirmed the course would return to the rota to host Europe's only major.
Martin Slumber's, Cheif Executive of the R&A said: "In light of today's decision by the honourable Company, we can confirm that Muirfield will become a venue for The Open once again.
Muirfield has a long and important history of hosting The Open and with today's announcement that will continue.
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 truely outstanding Open venue and we very much look forward to taking the Championship back there in the future"