Prime Minister Lee Hsien Loong, issued a statement before dawn announcing the passing of his 91-year-old father at the Singapore General Hospital following a long illness.
He declared seven days of national mourning until the former leader is cremated on 29 March.
"He fought for our independence, built a nation where there was none, and made us proud to be Singaporeans. We won't see another like him," the prime minister said in an emotional televised address.
Lee's remains will first be taken to the Istana state complex for a two-day private family wake before lying in state at Parliament House.
Singaporeans, some teary-eyed, flocked to the Istana to leave personal tributes and sign a condolence board.
US President Barack Obama led world leaders in hailing Lee, who turned a small territory lacking its own natural resources into a world player in finance, trading and shipping - all the while with a heavy political grip that was long decried by rights campaigners.
"He was a true giant of history who will be remembered for generations to come as the father of modern Singapore and as one of the great strategists of Asian affairs," Obama said in a statement.
China lauded Lee's "historic contributions" to their relationship after the Communist leadership embarked on dramatic economic reforms from 1978.
President Xi Jinping said Lee was "widely respected by the international community as a strategist and a statesman".
Tributes also came in from a host of international leaders including UN Secretary-General Ban Ki-moon and the prime ministers of Malaysia, Britain, Japan and Australia.
Lee, whose health rapidly deteriorated after his wife of 63 years, Kwa Geok Choo, died in 2010, was in hospital for nearly seven weeks with severe pneumonia.
Two years before he died, Lee revealed that he had signed an advance medical directive instructing doctors not to use any life-sustaining treatment if he could not be resuscitated.
He served as prime minister from 1959, when colonial ruler Britain granted self-rule, to 1990, leading Singapore to independence in 1965 after a brief and stormy union with Malaysia.
Singapore now has one of the world's highest per capita incomes and its residents enjoy near-universal home ownership, low crime rates and first-class infrastructure.
The opposition Workers' Party, whose leaders were among those harried for years by Lee under his authoritarian rule, joined the rest of the nation of 5.5 million people in mourning him.
"His contributions to Singapore will be remembered for generations to come," it said in a statement.
On the diplomatic front, Lee's counsel was often sought by Western leaders, particularly on China - which he identified early as a driver of world economic growth - as well as more volatile neighbours in Southeast Asia.
Singapore-based political analyst Derek da Cunha told AFP that "Lee Kuan Yew gave Singapore an international profile completely disproportionate to the country's size".
But the Cambridge-educated lawyer was also criticised for jailing political opponents and driving his critics to self-imposed exile or financial ruin as a result of costly libel suits.