Ofori-Atta, 57 and co-founder of the Africa-wide investment banking group Databank Group, was Akufo-Addo's nominee to assess the health of the economy during the transition period after the election.
Ghana which exports cocoa, gold and oil is halfway through a three-year $918 million aid deal with the International Monetary Fund to restore fiscal balance to an economy dogged by slumping growth, high deficit and public debt.
"Ken has the credentials of a successful economist and the president is set to name him as finance minister ... he's the guy to steer the economy out of the current challenges," said one aide with direct knowledge of the decision.
The announcement could come early this week, another aide said. "The new president is in a hurry to hit the ground running with the economy because there are expectations to meet," he said.
A graduate of Yale and Columbia universities, Ofori-Atta previously worked with Wall Street investment bank Salomon Brothers and Morgan Stanley on debt and equity management.