Vice-President Rupiah Banda, who is expected to take over as acting leader, made the announcement on state TV.
President Mwanawasa suffered the stroke at an African Union summit in Egypt and was then flown to France, where he had remained in hospital.
He came to prominence recently for being one of the African leaders most critical of the violence in Zimbabwe.
US President George W Bush expressed his condolences to Mr Mwanawasa's family, describing him as "a champion of democracy in his own country and throughout Africa".
French President Nicolas Sarkozy said Mr Mwanawasa's death was "a great loss for the African continent".
Former Zambian President Kenneth Kaunda said he had lost a "personal friend".
"He was a great leader. People loved him. We all loved him. He did great things," Mr Kaunda told the BBC.
Mr Mwanawasa's health was an issue during his presidency in 2002-2008.
In April 2006, he suffered a minor stroke four months before general elections.
"Fellow countrymen, with deep sorrow and grief, I would like to inform the people of Zambia that our President Dr Levy Patrick Mwanawasa died this morning at 1030 hours [0830 GMT]," Reuters news agency quotes Mr Banda as saying.
"I also wish to inform the nation that national mourning starts today and will be for seven days."
On Monday, Mr Banda said that the president's health had suddenly deteriorated and he had undergone emergency surgery.
Mr Mwanawasa was chairman of the South African Development Community (Sadc) when he was taken ill in June.
In that role he had been critical of the controversial election in Zimbabwe and had said he sympathised with Zimbabwean opposition leader Morgan Tsvangirai when he withdrew from the run-off because of attacks on his supporters.
Mr Mwanawasa won a second term in 2006, having campaigned on his economic record which won him acclaim from Western donors.
When he was vice-president in the 1990s he was involved in a near-fatal road accident which left him with slurred speech.
Mr Mwanawasa famously fell out with his predecessor, Frederick Chiluba, who had handpicked him to lead the ruling Movement for Multiparty Democracy.
He pressed for Mr Chiluba's immunity from prosecution to be lifted and the former president was charged with stealing money during his time in office.
His critics accused Mr Mwanawasa of persecuting his political rivals under the guise of fighting corruption.
He was married and had six children. He had been a practising lawyer since 1973.
In his most famous case, he defended former Vice-President Lt-Gen Christon Tembo and others who were charged in 1989 with plotting to overthrow Kenneth Kaunda.