De Klerk, who was also a key figure in the transition to democracy, had been diagnosed with cancer this year.
He was head of state between September 1989 and May 1994.
In 1990, he ordered Nelson Mandela's release from prison, leading to historic elections that brought the anti-apartheid leader to power.
De Klerk shared the Nobel Peace Prize with Mandela for helping to negotiate an end to apartheid. But his legacy divides opinion in South Africa.
A statement from the former president's FW de Klerk Foundation on Thursday said that he died peacefully at his home in Cape Town following his struggle against mesothelioma - a cancer that affects the lining of the lungs.
The foundation also released a video recording dubbed De Klerk's "final message" in which he talks about apartheid.
"Let me today, in the last message repeat: I, without qualification, apologise for the pain and the hurt, and the indignity, and the damage, to black, brown and Indians in South Africa," he says.
South African President Cyril Ramaphosa sent condolences to De Klerk's wife and children, and said the former leader's death "should inspire all of us to reflect on the birth of our democracy".
Ending apartheid
The former president was born in March 1936 in Johannesburg, into a line of Afrikaner National Party politicians.
He worked as a lawyer and served in a series of ministerial posts before taking over from PW Botha as the head of the National Party in February 1989, and months later becoming president.
In a famous speech to parliament the following year, he announced that he was removing the ban on parties that included Mandela's African National Congress (ANC).
He also announced that Mandela would be released from prison after 27 years.
His actions helped bring an end to apartheid-era South Africa, and he became one of the country's two deputy presidents after the multi-party elections in 1994 that saw Mandela become president.
He retired from politics in 1997, saying: "I am resigning because I am convinced it is in the best interest of the party and the country."
'Uneven legacy'
Although the relationship between De Klerk and Mandela was often punctuated by bitter disagreements, the new president described the man he succeeded as someone of great integrity.
In a statement on Thursday, the Nelson Mandela Foundation said De Klerk would "forever be linked to Nelson Mandela in the annals of South African history".
"De Klerk's legacy is a big one. It is also an uneven one, something South Africans are called to reckon with in this moment," the statement added.
Many have blamed De Klerk for violence committed against black South Africans and anti-apartheid activists during his time in power.
Last year, he became embroiled in a row in which he was accused of playing down the seriousness of apartheid. He later apologised for "quibbling" over the matter.
Human rights lawyer Howard Varney on Thursday described him as an "apologist for apartheid", while the Fort Calata Foundation - which campaigns for justice for people killed by the former white-minority regime - called him an "apartheid criminal".
In the video message released following his death, De Klerk says he has apologised on many occasions for "the pain and indignity that apartheid has brought to persons of colour in South Africa".
In his statement on Thursday, Mr Ramaphosa praised De Klerk for the "vital role" he played in South Africa's transition to democracy, despite "severe pressure to the contrary from many in his political constituency".
South Africa's main opposition party, the Democratic Alliance, said De Klerk's contribution to the country's transition to democracy could not be overstated.
"His decision, within a year of taking over the presidency... to unban liberation movements, release Nelson Mandela from prison, lift the ban on political marches and begin the four year negotiation process towards our first democratic election was a watershed moment in our country's history," party leader John Steenhuisen said.
