Lee, 91, the country's first Prime Minister, "passed away peacefully at the Singapore General Hospital," the government announced. He had been under intensive care for pneumonia since February 5.
In an emotional televised address, his son and current Prime Minister Lee Hsien Loong paid tributes to him.
"He fought for our independence, built a nation where there was none, and made us proud to be Singaporeans. We won't see another man like him."
Singapore declared seven days of national mourning and will hold a state funeral for him on March 29.
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The announcement of Lee's death in the early hours of the morning prompted a flurry of tributes from world leaders.
US President Barack Obama called Lee a "true giant of history" while UN secretary-general Ban Ki-moon described him a "legendary figure in Asia".
Chinese President Xi Jinping praised Lee as an "old friend of the Chinese people".
Xi said Lee, who was ethnically Chinese, was "widely respected by the international community as a strategist and a statesman" and expressed "sincere condolences".
The city-state's prime minister for 31 years, Lee was widely respected as the architect of Singapore's prosperity.
But the Cambridge-educated lawyer also attracted criticism for stifling media freedom and the harsh treatment of political opponents.
Born in 1923, Lee became Prime Minister in 1959 when Singapore, a small piece of land with no natural resources and a polyglot population of Chinese, Malays and Indians, was still British territory and beset by riots and unrest.
He presided over Singapore's bitter split from Malaysia in 1965.
A charismatic figure, Lee co-founded the People's Action Party (PAP), which has governed Singapore since 1959.
He quit as prime minister in 1990 but remained an influential figure in the government of Prime Minister Lee Hsien Loong, his eldest son.