Sinn Fein president Gerry Adams has secured his seat in Louth on the first count with more than 15,000 votes.
This was Mr Adams' first bid for election success in the Republic.
The declaration followed his dramatic decision to resign the West Belfast Westminster seat he first won in 1983, and to step down from the Assembly in the North, in order to enter southern Irish politics.
Mr Adams' strong poll showing came as his party was set to at least double its tally of five Dail seats.
The Sinn Fein president, who was hoisted on to the shoulders of jubilant supporters, said his party was set to make significant gains in the election.
"We went out in this election, we set out our stall very, very clearly," he said.
"I think the votes across the state show a significant amount of people support the position we have taken up."
He said he had sought only to win a seat and credited his election team with the poll-topping result.
After criticism of his performance in debating economic issues, he dismissed claims that this might resurface in the Dail.
"I don't have any concerns at all about that," he said.
"The people who are challenging me on our economic position are the people who brought the economy to its knees."
Mr Adams came under close scrutiny during his election campaign.
Victims of IRA violence raised objections to his bid to enter the Dail.
But his party colleague and Northern Ireland Deputy First Minister Martin McGuinness, who visited the Louth count centre to help mark his leader's victory, said his decision to run for office in the South had been vindicated.
"It is very heart-warming to be here and see that the people of Louth were able to see through all of that, all those who tried to undermine Gerry Adams' incredible contribution to peace in Ireland and to politics in Ireland," said Mr McGuinness.
"To be in a position to be elected in the first count, to top the poll, is an incredible result."