Fr Oliver Brennan was reinstated as a parish priest in Louth on Saturday night after two years under investigation.
The 67-year-old had voluntarily stepped down immediately as parish priest of Blackrock and Haggardstown in August 2010 when the allegation was made.
The Sunday Independent reports that a police investigation could find no evidence against Fr Brennan. The paper says the "allegations were totally lacking in credibility."
A Catholic Church inquiry into the allegations concluded they were ‘fabricated and have not been substantiated’.
Fr Brennan was reinstated at a special Mass in Blackrock, just outside Dundalk.
The paper reports that he is expected to be given a full apology by the church. Fr Brennan said: “My life has been on hold for two-and-a-half years. I’m glad this ordeal has ended. I’m looking forward to restarting my life in active ministry.”