A statement from his office said the 68-year-old died a few hours after being taken ill, but did not give details.
“It is with a heavy heart… that we announce the sudden and untimely death of the president of the Republic of Ghana,” the statement said.
Mr Atta Mills had ruled the West African country since 2009.
The BBC’s Sammy Darko, who is at the military hospital in Accra, says Mr Atta Mills’ voice has been degenerating in the last few months.
‘Rumours’
According to a presidential aide, the leader had complained of pains on Monday evening and died on Tuesday afternoon.
He had recently returned to Ghana after visiting the US for medical checks, the news agency says.
Vice-President John Dramani Mahama will be sworn in as president at 2000 GMT, in line with Ghana’s constitution.
Born on 21 July 1944 at Tarkwa in western Ghana, Mr Atta Mills graduated in law at the University of Ghana in 1967 before studying further at the London School of Economics and receiving a PhD from the School of Oriental and African Studies.
Mr Atta Mills later branched out into politics, becoming president after beating Nana Akufo-Addo in the 2008 elections.
It was third time lucky for Mr Atta Mills – the flagbearer of the National Democratic Congress (NDC) party – in his campaign to become president.