Welcoming his selection by 10 brother-bishops in the Catholic Abbey of Glenstal outside Limerick, Dr Brady praised Bishop Harper for always being a clear voice against division and sectarianism.
Meanwhile, the Presbyterian moderator, Dr David Clarke praised Bishop Harper's outstanding qualities which he displayed while leading the diocese of Connor, which emcompasses Co Antrim.
He described the 62-year old Englishman and father of four as 'a clear thinker able to identify what needs to be done in any situation'.
His leadership in Connor had proved he was 'a man of action and not just words', according to Dr Clarke.
Dr Harper said he was deeply humbled by the election.
It was announced at St Patrick's Cathedral by the Archbishop of Dublin, Dr John Neill, who said it would be a joy to work with someone who would bring great courage and clarity to the post.
Dr Robin Eames, who was head of the Church of Ireland for 20 years, announced his intention to retire at the end of 2006 last May.