Monsignor Treanor succeeds Bishop Patrick Walsh, who was in the post from April 1991.
Irish President Mary McAleese attended the ceremony.
The diocese is the second largest on the island of Ireland.
Monsignor Treanor, 57, is from Monaghan and was previously a parish priest in Clogher.
For the past 19 years, he has been based in Brussels working with the Commission of the Bishops' Conferences of the European Community.
He said the appointment marked a new and unexpected phase in his life.
The diocese covers Belfast and is the second largest in Ireland with a Catholic population of 330,000.
Reflecting on his appointment Msgr Treanor said there was promise in the air.
"Christians must lend their shoulders, their talents to building a society rooted in respect for the dignity of every human person and dedicated to pursuing justice for all, especially the underprivileged, the needy and the poor," he said. +++++++++++++++++++++++++++++++++++++++++++++++++++Disclaimer
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