Tighe was born in Navan, County Meath. He graduated from University College Dublin in 1979 with a BCL degree in Law. After studying for the priesthood in Holy Cross College in Clonliffe and at the Pontifical Irish College in Rome, he was ordained a priest of the Dublin Diocese in St. Laurence O'Toole Church in Kilmacud in 1983. His first appointment was as parish chaplain and teacher in Ballyfermot. Later, he studied Moral Theology at the Pontifical Gregorian University in Rome. Since 1990 he has been a lecturer in Moral Theology in the Mater Dei Institute of Education in Dublin. He was appointed head of the Theology department there in 2000.
In 2004, he was named the director of the Communications Office of the diocese of Dublin. He established its Office for Public Affairs, which aids communication between the diocese, government, public bodies and nongovernmental organizations in Ireland and Europe.
On 30 November 2007 Pope Benedict XVI appointed him secretary of the Pontifical Council for Social Communications, deputy to its President, Archbishop Claudio Maria Celli. Diarmuid Martin, Archbishop of Dublin, said: "Mgr Tighe is a priest of great competence and I am glad that he will have the possibility now to place his talents at the service of the Universal Church. I thank him for the service he has given to the Archdiocese of Dublin and wish him every success." Tighe said: "This appointment has come as a surprise to me. Communication of the Gospel must be at heart of the ministry of a priest and I am pleased to be asked to work in the Council that has a mandate to harness the potential of the media –new and old – as a means of evangelisation. I look forward to serving Pope Benedict XVI in his mission."
In an essay title "The challenge for the Church in a digital culture", Tighe wrote: "The generalized and uncritical social reception of the tenets of relativism finds particular expression in the digital world where the sheer volume of information and opinion, much of it contradictory, can lead to an almost resigned acceptance that it is meaningless to speak of truth and objectivity. In the face of so much assertion, argument and counter argument, it is difficult to decide where real authority and expertise resides".
On 9 July 2014 he was appointed secretary to the Committee for Vatican media, a special commission headed by Lord Patten of Barnes to recommend how to restructure the Vatican's communications efforts. At the conclusion of the committee's work, Tighe presented its conclusions to Pope Francis and the Council of Cardinal Advisers.
On 19 December 2015 Pope Francis appointed Tighe Adjunct Secretary of the Pontifical Council for Culture and Titular Bishop of Drivastum. He was consecrated as a bishop on 27 February 2016 by Cardinal Pietro Parolin, Secretary of State of the Holy See.
In 2017 Bishop Tighe spoke of the Church as a recognisable brand. He spoke at a 12 March panel titled “Compassionate Disruption” at the annual South by Southwest Festival in Austin. The panel was one of the festival’s first steps to address faith’s place in secular discussions. Bishop Paul Tighe, was on the panel with Catholic communicators Helen Osman, Michael Hertl and Christoph Krachten at the Hyatt Regency. The concept of branding has become more prevalent than ever, thanks to the digital age. All around the festival, commonly known as SXSW, companies marketed their brands via experiential booths and events.