"It is no secret that the president-elect and I have some pretty significant differences," Obama said from the White House, where he will meet Trump on Thursday. "We are now all rooting for his success."
Obama, who campaigned for Democratic colleague Hillary Clinton, repeatedly slammed Trump about his fitness to hold the office. Trump harshly criticized Obama almost daily and aims to repeal his hallmark Affordable Care Act when he takes office.
But Obama said he respects a peaceful transition of power to Trump despite political sparring in a "long and hard fought campaign." He said he hopes Trump maintains a spirit of "unity," "inclusion" and "respect for our institutions" throughout the transition.
Obama added that he "could not be prouder" of Clinton, who served as secretary of state in his first term.
"She has lived an extraordinary life of public service," Obama said.
Obama's remarks came shortly after Clinton publicly congratulated Trump and told her supporters they owe Trump an "open mind."
"We have seen that our nation is more deeply divided than we thought. But I still believe in America and I always will. And if you do, then we must accept this result and then look to the future. We owe him an open mind and the chance to lead," Clinton said.
Obama also tried to assuage young voters who may have cast a ballot for the first time and were disappointed in the outcome. He told them not to "get cynical" and "think you can't make a difference."
Trump's surprise victory was fueled by apparent wins in the swings states of Florida, North Carolina, Ohio and Pennsylvania. Trump has a projected 279 electoral votes with three states left to be called by NBC. NBC said Clinton appeared to have the popular vote by 189,000.