He was educated at Saint Ignatius' College, Riverview and studied economics and law at the University of Sydney.

He then studied for two years at the Gregorian Pontifical University in Rome, obtaining a Licentiate in Fundamental Theology.

From 2012 to 2014, he served as the administrator at the Sacred Heart Cathedral in Broken Hill, New South Wales, within the Diocese of Wilcannia–Forbes.

Meagher was appointed Auxiliary Bishop of Sydney by Pope Francis on 18 November 2021 and was given the titular see of Pocofelto in Tunisia.

He was consecrated by Archbishop Anthony Fisher on 8 December 2021 in St Mary's Cathedral, Sydney.