The Speculative Society was founded in 1764 “for improvement in literary composition and public speaking”.
It is one of the oldest debating societies in the world and can count high-profile figures including former prime minister Sir Alec Douglas-Home, the Duke of Edinburgh and Sir Nicholas Fairbairn among its ranks.
It has been holding secretive men-only meetings at the University of Edinburgh for two and a half centuries.
But all that is set to change after a poll held in February saw members vote three to one in favour of allowing women to join.
The Spec, as it is known to members, meets in three rooms in Edinburgh University’s Old College but has no formal links to the institution.
However, the university last year pledged to “review its relationship” with the club after it was revealed that no rent or rates were paid in exchange for the accommodation.
Membership is by invitation only, and, although there are no rules barring females, none has ever been admitted.
A report by Professor Mary Bownes, the university’s vice-principal community development, identified a “lack of alignment” between the Spec’s all-male membership and the institution’s “clearly stated commitment to equality and diversity”.
It recommended the club should be given six months to admit females and to open its meeting rooms to the public – “especially on open days”.
It also stated that any future agreement on the society’s position within university grounds should be “clear and open”.
It did not outline what would happen if the arcane organisation failed to comply once the deadline had expired.
The Spec, whose membership is believed to include leading Scottish lawyers and academics, was one of the last remaining male-only organisations north of the Border.
The Royal & Ancient Golf Club of St Andrews voted last autumn to extend its membership to women, reversing a tradition going back 260 years.
Women will be permitted to take part in Spec gatherings from this autumn, when the new session gets under way.
A spokesman said: “A consultation of our membership was concluded in February, with members voting three to one in favour of admitting women.
“We have welcomed female candidates for membership since then and expect to admit female members in the next session, which begins in October.
“We hope that our newly established position on female membership will strengthen the society and enable us to continue our 250-year-old tradition of advancing public speaking and literary composition long into the future.”
He insisted the group had “actively discussed female membership for many years”.
The Spec was forced to cancel a 250th anniversary celebration due to be held in Old College last winter after students planned a picket over the university’s links with its “all-male elite”.
A statement from protesters said: “Senior management are making a clear choice to privilege the interests of an all-male elite over the concerns of students about equality. We need to make it clear this isn’t the kind of university or community we want to be part of.”
University leaders welcomed the move. Prof Bownes said: “This is a positive change.”