He passed away at 3:18am local time (3:18pm EDT) at Singapore General Hospital, where he had been admitted on February 5 suffering from pneumonia.
Thousands of people had been leaving flowers and cards at the hospital over the past three days, praying for his recovery, and many rushed back there when they awoke to the news of his death.
Lee had receded from public and political life over the past few years, but he was still seen as an influential figure in the government of Prime Minister Lee Hsien Loong, his oldest son.
In his lifetime, Lee drew praise for his market-friendly policies but also criticism at home and abroad for his strict controls over the press, public protest and political opponents.
The government has declared a period of national mourning until his funeral on March 22. Lee's family will hold a private wake in the next two days, then his body will lie in state at parliament from Wednesday to Saturday.
Lee became Singapore's first prime minister in 1959 and held onto power for 31 years, overseeing the island's transformation from a port city battling crime and poverty into one of Asia's most prosperous nations.
Even after stepping down as leader in 1990 - signing off as the world's then longest-serving prime minister - the acerbic Lee stayed on in the cabinet until 2011. He was a member of parliament until his death.
His leadership of Singapore was seen as a model for developing countries across the world, and politicians of all stripes said they took inspiration from his policies.