Mahama, the former vice president, had been interim president since July following the death of President John Atta Mills, then won an election in December -- an outcome that has been challenged by the opposition, CITI-FM radio reported.
"I will work hard to place us on the right path and I will lead us over the hurdles and pass the obstacles that might threaten to keep us from meeting our goal," Mahama said.
Tens of thousands of spectators heard Mahama's speech at Independence Square and several heads of African states were in attendance, Ghana Broadcasting Corp. reported.
Members of the opposition New Patriotic Party were not in attendance. NPP leaders had warned members to stay away so as not to undermine the party's challenge of the election results -- now before the Supreme Court.
Mahama was elected with 50.7 percent of the vote, a 3 percent margin of victory over the NPP candidate, Nana Akudo-Addo.