Archbishop Justin has been critical of Trump in the past, once saying it would be "very challenging" is he was to take the White House.
The billionaire businessman will become the 45th president of the United States after voters gambled on his pledge to "Make America Great Again".
Speaking at a victory party in New York after rival Hillary Clinton conceded defeat, Mr Trump urged Americans to put the election behind them.
In a statement posted on Twitter, Archbishop Justin said his continuing prayers were that the United States would find reconciliation after a "bitter campaign".
He said: "As President-elect Donald Trump prepares to take office, my continuing prayers are that the United States of America may find reconciliation after a bitter campaign, and that Mr Trump may be given wisdom, insight and grace as he faces the tasks before him. Together we pray for all the people of the United States."
Previously the leader of the Anglican Church had criticised Trump's policy of halting the immigration of Muslims to the United States.
It was "certainly not a Christian thing to do, nor is it a rational thing to do," he told MPs in June.
Elsewhere the Catholic Church expressed its "best wishes to the new president".
In a statement, translated from Italian by news agency Zenit, Vatican Secretary of State Cardinal Pietro Parolin said: "First of all, we must note with respect the will expressed by the American people in this exercise of democracy that they tell me was also characterized by a large turnout.
"We give our best wishes to the new president, so that his government can be really fruitful and also we assure him of our prayers, so that the Lord may enlighten him and support him in service of his country, and of course, also in serving the well-being and peace in the world.
"I think that today there is a need for everyone to work to change the world's situation, that is one of severe laceration, and of serious conflict."
