The poll forecasts Mr Higgins will win by 56 percent.
A second exit poll, by Ireland’s national broadcaster RTE, also suggests Mr Higgins will be re-elected for another term as the country’s President.
Mr Higgins tweeted: “The polls have closed and we want to thank everyone for all your help.
“We don’t know the outcome yet, but we do know we could not have run this campaign without you.
“Thank you.”
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The poll was conducted using 4,365 respondents outside 160 polling stations across the country on Friday.
Its accuracy is estimated at +/- 1.5 percent.
Peter Casey is expected to finish second with a 21 percent share of the vote.
Opinion polls during the early stages of the campaign showed there to be little support for Mr Casey.
However, after his extensive criticism of Travellers and claims there is growing welfare dependency in Ireland, support appears to have surged towards the entrepreneur.
Some pollsters even reported Mr Casey was receiving as many votes as Mr Higgins.
Support for other candidates was low.
Seán Gallagher, who won half a million votes in 2011, failed to make any headway according to the poll.
The statistics show he is likely to end with just seven percent of the vote – 22 percentage points less than his 2011 share.
Sinn Féin’s candidate, Liadh Ní Riada, received a disappointing eight percent of the vote according to the poll.
This reflects just a third of the party’s current support in the most recent Ipsos MRBI Opinion poll.