President John Mahama called Mr Akufo-Addo to admit defeat, a spokesman for his party said, as the Electoral Commission announced the result.
Celebrations have broken out in the capital, Accra.
Mr Akufo-Addo, from the New Patriotic Party, won the election on his third attempt to reach the presidency, after a campaign dominated by the country’s faltering economy.
“I make this solemn pledge to you tonight: I will not let you down,” he told a jubilant crowd in front of his residence.
“I will do all in my power to live up to your hopes and expectations.”
Ghana’s Electoral Commission (EC) declared Mr Akufo-Addo the winner, with 53.85% of the votes, while Mr Mahama took 44.40%. Turnout was at 68.62%.