Bishop Corbett was born in Limerick, Ireland on July 12, 1834. He was the eldest child of James Corbett and his second wife, Catherine, nee Reeves.
He began his education at CBC, Limerick. After completing his secondary education at Cambrai, France, he studied priesthood at Bruges, Belgium and Le Mans, France.
He was ordained in France on May 29, 1858 as a priest of the Diocese of Limerick. However, historical documentation for this appears to have been destroyed in subsequent wars.
After five years in Limerick, he answered the call of Archbishop James Francis Alipius Goold for priests to come to the new Australian state of Victoria. He arrived on the sailing ship, Lightning, on August 29, 1863.
He was Archbishop Goold's private secretary for many years, during which time he was also in charge of the St Kilda Mission. In 1879, Fr Corbett was appointed Chancellor and Vicar General of Melbourne Archdiocese.
Pope Leo XIII appointed him as the first Bishop of Sale on May 13, 1887, eight days after the creation of the Diocese of Sale.
He was consecrated a bishop on August 25, 1887 at St Mary's Church, East St Kilda by Archbishop Thomas Joseph Carr of Melbourne. Co-consecrators were Bishop Daniel Murphy of Hobart, and Bishop James Moore of Ballarat.
Bishop Corbett was regarded as an authority on Canon Law and liturgy. In 1885, he was appointed assistant secretary to the Plenary Council of Australia. On October 27, 1897 he had the honour of consecrating St Patrick's Cathedral, Melbourne, and after 1907 he was the senior priest in Victoria.
He was awarded the Papal Order of the Holy Sepulchre and the Pilgrim's Cross of Jerusalem and in 1911 Pope Pius X appointed him Assistant Bishop at the Papal Throne.
Bishop Corbett died in St Helen's Hospital, Sale, on May 29, 1912. He is buried in front of Our Lady's Chapel in St Mary's Cathedral, Sale.
His Coat of Arms features the motto “Monstra te Esse Matrem” which is taken from the fourth verse of Hail Star of the Sea (Ave Maria Stella) and translates as “Show yourself to be a Mother.”
The Arms feature a representation of Our Lady of Perpetual Succour on the left hand side and a raven on the right which is believed to be a play on words between the raven genus corvid and Corbett.