The pontiff granted Spanish Monsignor Lucio Vallejo Balda a Christmas-time clemency after he served half of his 18-month sentence, the Vatican said.
The priest was convicted in July. The leaked papers were cited in books published in 2015, that alleged corruption in the Catholic Church.
A former colleague of the priest was given a 10-month suspended sentence.
On Tuesday, the Vatican said in a statement that Pope Francis granted "conditional freedom" to Mgr Angelo Lucio Vallejo Balda.
"This is a clemency measure which allows him to regain his freedom. The penalty is not quashed."
The statement added that all his professional ties to the Vatican had ended, and he would now be under the authority of the Bishop of Astorga in Spain - the priest's original diocese.
Mgr Balda has made no public comment on the latest developments.
The books, by journalists Emiliano Fittipaldi and Gianluigi Nuzzi, were based on leaked materials and exposed waste and financial mismanagement in the Church.
The original Vatileaks episode saw the last Pope's former butler, Paolo Gabriele, sentenced to 18 months in jail in 2012 after being found guilty of stealing sensitive documents from the pontiff's desk.
He served nearly three months of his sentence under house arrest in the Vatican before Pope Benedict visited him and personally pardoned him.
The Vatican has only two prison cells but it can ask Italy to house its prisoners under the terms of a 1929 treaty.
Pope Francis has freed a priest jailed for leaking official documents in a trial known as Vatileaks II.