The Pontiff is indefinitely extending permission he gave during the recent Holy Year of Mercy which allowed all priests to declare such women free of guilt.
He said: "Lest any obstacle arise between the request for reconciliation and God's forgiveness, I henceforth grant to all priests, in virtue of their ministry, the faculty to absolve those who have committed the sin of procured abortion."
Prior to the Holy Year of Mercy, which ended on Sunday, the ability to absolve women who have undergone the termination of a pregnancy was reserved for bishops and special confessors.
In an Apostolic Letter released by the Vatican on Monday, Pope Francis went on to say: "There is no sin that God's mercy cannot reach and wipe away when it finds a repentant heart seeking to be reconciled [with God]."
Cementing his position on abortion, he added: "I wish to restate as firmly as I can that abortion is a grave sin, since it puts an end to an innocent life."