President Michael D Higgins wished Pope Francis well in his pontificate, expressing his "sincere best wishes" on behalf of the people of Ireland.
In a message to the new pontiff, Mr Higgins said his election would "no doubt bring great joy to the people of Argentina and of South America, as well to the Jesuit community worldwide".
He said that despite the “pressures and distractions of a more complex world”, people everywhere still yearned for a sense of spiritual meaning to their lives.
“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,” Mr Higgins said in a statement.
'Peace and joy'
"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."
He said he looked forward to meeting Pope Francis.
Taoiseach Enda Kenny congratulated the new pope and said he had the best wishes of all Irish people as he took on “the immense responsibility” of his pontificate.
"We pray that he will have the strength, the good health and the spiritual guidance needed to lead the Catholic Church in the many challenges it faces," he said.
Mr Kenny said the conclave's choice of the first pope from the Americas was a symbolic expression of the global nature of the Catholic Church and of the 21st century world. "The people of Ireland also send our congratulations to the people of Argentina, a country with which Ireland shares many historic bonds, on this occasion of great honour and pride for their nation," he added.
Archbishop of Dublin Diarmuid Martin said he reacted with "surprise and delight" on hearing the news of Cardinal Bergoglio 's election.
Dr Martin said Cardinal Bergoglio had an interest in Ireland and recalled a long conversation they once had. "He asked me a lot about Dublin, what was happening at the time. He told me he was following it and he was very supportive," the archbishop told The Irish Times.
Dr Martin described the new pope as a man who lived his life simply, but who spoke with a striking clarity.
“There was an incident in 2012 where some priests felt that the children of unwed parents or single mothers shouldn’t be baptised. He gave an extraordinary homily in which he said, ‘This is the hypocrisy of today, this is the clericalisation of the church, these are the people who want to keep God’s people from salvation’. He used phrases like ‘no to clerical hypocrisy, no to mundane spirituality’. This was to his priests.”
The archbishop also pointed to the choice of Francis as the new pope’s name.
“ Francis of Assisi . . . was a poor man, a spiritual person who wanted to reform a difficult church at the time, not through structural reform but through holiness and simplicity of life,” he said. “Cardinal Bergoglio is renowned for the simplicity of his life.”