Fr Paul Morton, of St Bride's RC church in Cambuslang, South Lanarkshire, was interviewed by police following the allegations and suspended by the Catholic Church.
Officers have now told the priest they are taking no further action and he has been cleared of the accusations.
The 55-year-old was also told to leave the attached parish house.
In a statement to Premier the Catholic Church said Bishop Joseph Toal had met with Fr Morton to discuss his future.
It's understood the Diocese of Motherwell has now started a process within the Church that could bring the priest back to ministry at St Bride's.
Bishop Toal said: "We will all require to be patient during this process, which is the prescribed way to proceed.
"I pray that this case will quickly proceed to a just conclusion and we will be able to welcome Fr Morton back to active ministry."
A Police Scotland spokesman said: "We can confirm that police have carried out an investigation following a report of historical sex abuse.
"No further police action will be taken at this time."
It's understood many parishioners had been keen for the priest to return with one telling Premier: "Fr Morton has been completely exonerated, I have never doubted Fr's innocence."