The 70-year-old, who had served as leader of Scotland’s largest Catholic community since 2012, tested positive for Covid-19 shortly after Christmas and had been self-isolating at home.
He died on Wednesday, January 13, being the Feast of St Mungo – the patron saint of Glasgow.
In a statement, the Church said: “A statement said: “It is with the greatest sorrow that we announce the death of our Archbishop.
“The Archbishop of Glasgow, Philip Tartaglia, has died suddenly at his home in Glasgow. He was 70 years old.”
“Archbishop Tartaglia, who had served as Archbishop of Glasgow since 2012, had tested positive for COVID 19 shortly after Christmas and was self-isolating at home.
“The cause of death is not yet clear.
“The Archbishop had served as leader of Scotland’s largest Catholic community since 2012.
“The Pope’s Ambassador to Great Britain, Archbishop Claudio Gugerotti has been informed.
“It will be for Pope Francis to appoint a new Archbishop to succeed Archbishop Tartaglia, but until then the Archdiocese will be overseen by an administrator.”
On Facebook, a spokesperson for the St Thomas the Apostle Riddrie church said: “East End Dean, Canon Andrew McKenzie called at midday today (13 January) with the sudden, shock, news that his Grace, the Archbishop, Most Reverend Philip Tartaglia, has died.
“He spent time at school in this parish and this place was dear to him.
“Please pray for the eternal repose of his soul.
“The parish has no further information at this moment and with you awaits an official statement from the Archdiocese.”
Parish Priest of Saint Augustine’s Roman Catholic Church in the Diocese of Motherwell, Scotland, Father Michael J Kane added: “Please pray for the repose of the soul of Archbishop Philip Tartaglia who sadly died this morning.
“We pray for the intercession of St Mungo, patron saint of Glasgow whose feast day we celebrate today. May he watch over the clergy & people of the Archdiocese at this sad time.