Canon Liam Devine also said relations between England and Ireland have never been better, and he was "delighted" to see the two meet.
He was speaking after the Prince Charles embarked on a four-day tour of Ireland, where he publicly met and shook hands with Gerry Adams.
The meeting is significant because no royal has never met with Gerry Adams before, and because the IRA - which has links to Sinn Fein - assassinated Prince Charles' great uncle Lord Mountbatten in Mullaghmore, County Sligo, in 1979.
It was part of The Irish Troubles, which saw predominantly Catholic republican paramilitaries and mostly Protestant unionist paramilitaries fighting against each other for decades.
Canon Devine, from the Diocese of Elphin where the murder took place, told Premier's News Hour: "It's a wonderful breakthrough.
"I'm delighted and indeed the royal family... are very, very welcome here to Ireland.
"I think they will experience a royal Irish welcome, if you can put it that way.
"We have a whole new generation of Irish people growing up now who have forgotten The Troubles and scarcely know what they were about.
"We have a whole new climate of opinion and I think the relations in the country were never better between Ireland and England at the present time.
"I couldn't have imagined this happening ten years ago you know, given his [Gerry Adam's] past and the record of the IRA and Sinn Fein, but it's a major breakthrough I think and it's wonderful.
"That's the road to go, the road of reconciliation and forgiveness, and let the past be the past and let us begin again and let us go forward."
Listen to Canon Liam Devine speaking to Premier's Des Busteed on the News Hour:
