The President-elect has said he will continue his predecessor's work to help heal the wounds of the Troubles.
Mary McAleese's historic period as head of state included efforts to build bridges between Protestant and Catholic communities.
Michael D Higgins told a press conference in Dublin, following the confirmation of his election, that he wanted to continue in that task.
The man who will be Ireland's ninth president said his humanitarian work overseas had taught him that, even after peace has been established, continued efforts are required to repair divided societies.
His comments came as political and religious leaders in Northern Ireland welcomed his election.
Alliance party leader and Stormont Justice Minister David Ford congratulated Mr Higgins. "I look forward to close co-operation with him and I believe it is very important that strong North-South links exist," he said. "Michael D Higgins fought a strong, positive election campaign. I am sure he will continue that positive message in the Presidency, building on the work of Mary Robinson and Mary McAleese.
"I also wish to take this opportunity to praise Mary McAleese on the excellent work she has done in her time as President and wish her well for the future. Mary McAleese has helped build and maintain excellent North-South relations and I want to commend her on everything that she has achieved in this role."
Ulster Unionist leader Tom Elliott sent his best wishes even before the winner's success was formally confirmed.
"I am confident that he will build on the legacy left by his predecessor, and continue the work of building bridges and helping to create better understanding based on mutual respect," he said. "I look forward to working with him on matters of mutual benefit to both Northern Ireland and the Republic."
Church of Ireland Primate, the Most Revd Alan Harper, added his congratulations. "The people of the Republic have conferred on him both a great honour and a great responsibility at a crucial moment in the history of Ireland," he said. "I not only wish Mr Higgins well as he prepares to take up his new responsibilities but also look forward to the unveiling of the particular insights and special personal gifts he will bring to the discharge of the office of President."