Ledwich was born in Dublin and educated at Trinity College, Dublin.[2] Ledwich was a prebendary of Christ Church Cathedral, Dublin from 1749 to 1781; 4th Canon of Kildare Cathedral from October to December 1760;[3] Treasurer of Kildare Cathedral from 1760 to 1772;[4] Archdeacon of Kildare from 1765 to 1772;[5] and Dean of Kildare from 1772 until his death.[6]