President Michael D Higgins has conveyed his sincere best wishes to the new head of the Catholic Church.
Jorge Bergoglio, an Argentine cardinal of Italian descent, was elected Pope on the conclave's fifth ballot. The Jesuit will take the name Pope Francis.
In his message, President Higgins conveyed the best wishes of the people of Ireland to the 76-year-old as he assumed the office of Holy Father.
"Despite the pressures and distractions of a more complex world, people all over the globe still yearn for a sense of spiritual meaning to their lives," said Mr Higgins.
"Your leadership of the church will therefore be of immense importance in providing ethical guidance and moral encouragement towards a world that is more just, more compassionate and more focused on a shared sense of community.
"While your election to this challenging ministry of service brings great personal responsibilities, I sincerely hope it will also offer opportunities for peace and joy as you carry out your duties in solidarity with the wider church community."
Mr Higgins said the election will bring great joy to the people of Argentina and of South America, as well as to the Jesuit community worldwide. He added: "I look forward to meeting you in person at an appropriate opportunity in the future."
Cardinal Bergoglio, who was regarded as a surprise choice, is the first Jesuit, as well as the first from the Americas and the first from outside Europe in more than a millennium. His dramatic election was signalled when white smoke billowed from the conclave of cardinals meeting in the Sistine Chapel in Rome.
Taoiseach Enda Kenny said the scenes of celebration in St Peter's Square are a reflection of the great hopes and best wishes that people of the Catholic faith all around the world have for the new pope.
"On behalf of the Government and the people of Ireland, I offer warm congratulations to Cardinal Jorge Mario Bergoglio on his election as Pope Francis," he said. "He has the best wishes of all Irish people, of all traditions, as he undertakes the immense responsibility of his pontificate."