Father Dermot Keaveney, 72, of Beacon Hill, Hindhead, Surrey, was convicted at Lewes Crown Court of offences which took place more than 30 years ago.
He was serving as a priest at various churches in Brighton and Hove, in East Sussex, at the time of the crimes.
Keaveney, who had denied the charges, was remanded in custody for sentencing on 13 November.
He was convicted of 15 counts of indecent assault and serious sexual offences between 1975 and 1982 following a two-week trial.
"We hope that the case brings some closure to the brothers who suffered Keaveney's abuse and their immediate families"
The court heard Keaveney repeatedly abused the boys, who were aged between 11 and 15 at the time of the assaults.
Jurors heard he gave the boys treats and took them on day trips and holidays before sexually abusing them and asking them not to tell anyone.
During the trial, Keaveney had insisted he had been giving the boys and their family support.
Judge Paul Tain told Keaveney that he would be remanded in custody because of the severity of his crimes and amid concerns that he would flee.
Speaking afterwards, Det Con Darren Grimes, of Sussex Police, said: "We worked in close co-operation with the Diocese of Arundel and Brighton and our determination to bring this case to justice, despite the passage of time, is reflected in today's result at court.
"We hope that the case brings some closure to the brothers who suffered Keaveney's abuse and their immediate families."
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