Higgins, a Labor Party candidate, had won 39.6 percent of first-preference votes in Ireland's electoral system, The Daily Telegraph reported.
Gallagher, who had been Higgins' main rival and held a lead going into the final week of the campaign, conceded defeat and congratulated Higgins Friday.
"In the last hour, I've called Michael D. Higgins to congratulate him on his performance and his success in this election," Gallagher said in a statement. "He will have my full support as president and I sincerely thank him for a positive campaign. His slogan stated that he would be a president to be proud of and I believe he will be that president."
Gallagher lost his lead after McGuinness accused him in a live, televised debate Monday of collecting a $7,080 donation from a convicted criminal.
Gallagher denied the claim and accused McGuinness of a "political assassination" attempt.
Higgins will succeed Belfast native Mary McAleese, who served two seven-year terms. He had been a member of Parliament since the early 1980s and has written two volumes of poetry.
Independent Sen. David Norris, the first openly gay presidential candidate, was expected to finish fourth.
Voter turnout was at 56 percent in the election, in which voters rank candidates in order of preference and candidates are eliminated one at a time and their votes redistributed until one has an absolute majority.
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need