The Electoral Commission (EC) said the results were delayed because supporters of the two main parties disrupted the process and asked the police to clear the data collection centers.
Mahama supporters took to the streets to celebrate across the country.
Bawumia said he was basing his statement on the results of internal calculations by the ruling New Patriotic Party (NPP).
He said it showed that Mahama won “decisively” while the opposition National Democratic Congress (NDC) also won the parliamentary election.
President Nana Akufa-Addo is stepping down after reaching the official limit of two terms in office.
Mahama, 65, previously led Ghana from 2012 to 2017, when he was succeeded by Akufa-Addo.
His previous time in office was marred by a deteriorating economy, frequent power outages and corruption scandals.
However, Ghanaians hope that this time things will be different.
