He said his government would distance itself by allowing an independent prosecutor to investigate cases and make its own decisions.
Mr Akufo-Addo defeated incumbent John Dramani Mahama in last week's election.
Mr Mahama has been accused of not tackling a series of corruption scandals.
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In an interview with the BBC's Akwasi Sarpong in his home in Accra, Mr Akufo-Addo outlined how he intended to deliver the promises he made to Ghanaians which earned him the presidency.
"As a matter of principle, we have decided to take the politics out of it, so that screams of witch-hunting ... don't arise, by establishing an office of special prosecutor," he said.
He said the prosecutor would be "somebody who will be independent of the executive and whose remit will be to investigate and tackle issues of corruption".
He also warned that people in his government would not be "immune from investigation merely because we are politicians".
Mr Akufo-Addo is to be sworn in on 7 January.
He gained 54% of the vote, while Mr Mahama took 44%.
He had been defeated in the two previous elections.
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Ghana's President-elect Nana Akufo-Addo says he will set up a special team to investigate corruption but said it would not be a "witch-hunt".