Father Robert Mackenzie, 87, had been accused of committing offences at two Catholic boarding schools.
The 18 charges involved allegations of physical and sexual abuse at Fort Augustus Abbey in the Highlands and Carlekemp Preparatory School in North Berwick between 1955 and 1988.
Fr Mackenzie had denied the allegations and it is understood he planned to plead not guilty when the case came to trial
However, the Crown Office and Procurator Fiscal Service (COPFS) has confirmed there will should be no further proceedings.
One of the complainers, David Walls, told BBC Scotland that he asked for the decision to be reviewed but it was upheld and the charges against Fr Mackenzie have been withdrawn.
Mr Walls said: "My gut reaction is very complex. Disappointment, to put it mildly.
"I'm disappointed in the justice system, because justice isn't about putting criminals behind bars, as much as it is for delivering the truth for the victims of the alleged crimes.
Edinburgh-born Fr Mackenzie taught at Carlekemp during two spells between the 1950s and 1970s, and was a teacher and housemaster at Fort Augustus between 1977 and 1988.
He worked in Saskatchewan before retiring in Canada and was flown to Scotland after a warrant was issued for his arrest in 2017.
Fr Mackenzie denied the allegations but the extradition was approved by Canada's Minister of Justice.
He was sent to Scotland in 2020 and held in custody for 13 months before he was released on bail in March 2021.
In a statement, COPFS said it would not be appropriate to give its reasons for dropping the charges "to respect the rights of all of those involved in the case."
The procurator fiscal for High Court Sexual Offences Fraser Gibson said: "This has been a complex investigation and the Crown Office and Procurator Fiscal Service appreciates that it has been a difficult time for all those involved.
"Following a detailed review of the facts and circumstances of the case, proceedings are now at an end."
Allegations that children suffered sexual and physical abuse at Fort Augustus and Carlekemp first emerged in a BBC documentary in 2013. Both schools closed decades ago.
The programme led to a police investigation and was a major factor in the Scottish Government's decision to hold a public inquiry into the historic abuse of children in care.
The judge presiding over the Scottish Child Abuse Inquiry later concluded that Fort Augustus and Carlekemp had been "havens for paedophiles where they had easy access to their chosen victims." Lady Smith said children had also suffered brutal physical abuse at both schools.
Two former priests who worked at Fort Augustus have been convicted in the courts.
And in November, a former Catholic monk was jailed for seven years for a catalogue of abuse and brutality at residential schools.
Michael Murphy, 88, was convicted of 29 offences of assault, indecent assault and indecent conduct against boys at St Ninian's List D School, at Gartmore, in Stirlingshire, and St Joseph's School in Tranent, in East Lothian.