Doherty and his victim were met off the train by officers from the British Transport Police.
The man did not initially tell officers he had been touched by Doherty, as the priest was standing nearby.
However, in a report to police two days later he said he had woken up “several times” while being abused.
Procurator fiscal Helen Nisbet said: “Daniel Doherty committed these serious sexual offences while holding a position of trust within his community.
“His predatory behaviour was brought to light thanks to the courage of the victim coming forward and reporting it to the authorities.”
Doherty left the priesthood following the allegations.
The Archdiocese of St Andrews and Edinburgh has offered a “profound apology” to his victim.
Doherty was also placed on the sex offenders’ register for 10 years.
