Francis took the step because Monsignor Lucio Vallejo Balda had already served more than half of his 18-month sentence, Vatican Radio said, quoting a Vatican press statement.
Balda will be under "conditional freedom" for the rest of his sentence, will leave his post at the Vatican and be put under the jurisdiction of the diocese of Astorga in his native Spain, the statement said.
Balda was jailed in July after the controversial trial at the Vatican that saw him, his assistant, two investigative Italian journalists and a PR consultant in the dock.
The case centred on the documents used by the journalists for their books exposing corruption, waste and financial mismanagement at the highest levels of the church.
Italian public relations expert Francesca Chaouqui was given a 10-month suspended sentence while the journalists and Balda`s assistant were cleared.
The journalists` prosecution was widely criticised as a move harming freedom of speech and information.
Chaouqui and Balda had been appointed by Francis to a now-defunction papal reform commission probing the Vatican`s finances.
Francis`s act of clemency at Christmas is reminiscent of when his predecessor Emeritus Pope Benedict XVI pardoned his former butler Paolo Gabriele in December 2012.
Gabriele was jailed for leaking some of Benedict`s private correspondence to Italian media in what was known as the first `Vatileaks` case.