The 85-year-old had been diagnosed with cancer earlier this year.
He came to power in 1989 under apartheid, a system of legalised racism, but later became a key figure in the transition to democracy.
He ordered Nelson Mandela's release from prison, leading to historic polls where the anti-apartheid leader became the first black president.
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.
Following his death, the FW de Klerk Foundation released a video recording - dubbed his "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.
The foundation said De Klerk had died peacefully at his home following his struggle against mesothelioma - a cancer that affects the lining of the lungs.
South African President Cyril Ramaphosa said De Klerk's death "should inspire all of us to reflect on the birth of our democracy".