For centuries, the various departments have been led by male priests, usually cardinals or bishops, but that may change from June 5, when the new charter enters into force after more than nine years of development work.
The new constitution does not differentiate between lay men and women, although experts believe that at least two wards - the one for bishops and for clergy - will remain led by men because only men can be priests in the Catholic Church.
Francis has already appointed a number of Catholics, including women, to the Vatican Department.
Women in the Vatican
Last year, the pope appointed a woman to the second position in the Vatican's governorship for the first time, making Sister Raffaella Petrini the highest-ranked woman in the world's smallest state.
In addition, he appointed Italian nun sister Alessandra Smerilli to the interim post of secretary of the Vatican's Development Office, which works on law and peace issues.
In addition, Francis has appointed Nathalie Becquart of France as co-secretary of the Synod of Bishops, which prepares large meetings with world bishops held every few years.
The Pope's ninth anniversary
The 54-page constitution, called the Preaching Gospel, was released on the ninth anniversary of Francis' inauguration as pope in 2013, replacing one issued in 1988 by Pope John Paul II.