Lee, 91, had been hospitalized since Feb. 5 for pneumonia and recently had been on life support. He "passed away peacefully'' early Monday, the prime minister's office said.
Lee led Singapore from 1959 to 1990 and remained a member of parliament after leaving the office of prime minister. His son, Lee Hsien Loong, is Singapore's third and current prime minster, and the small nation is celebrating its 50th anniversary of independence this year.
The prime minister declared a period of mourning, from Monday to Sunday, with flags at half-staff.
"We won't see another man like him,'' Lee Hsien Loong said in a televised address to the nation of 5.4 million million people. "To many Singaporeans, and indeed others too, Lee Kuan Yew was Singapore.''
Singapore, with its British heritage, became a major player in global shipping with its strategic location at the Singapore Strait and Port of Singapore, and it has achieved one of the highest per-capital gross domestic products in the world.
Under Lee, Singapore also became known for the government's authoritarian rule, strict law enforcement and limits on public protests. The government justified the tactics as necessary to remain stable and independent, given its location surrounded by the large Islamic nations of Malaysia and Indonesia.
That strict rule was reflected in the clean, modern and affluent city that Singapore became. With low taxes, good schools, low crime and investment-friendly laws, Singapore became a popular place for western companies, including many European businesses, to base their employees and operations focused on Southeast Asia and East Asia.
The authoritarian rule drew global criticism as well, however, as it allowed Lee to exert strong control over the country. Some political rivals were jailed, and Singapore aggressively used the courts to silence journalists and opposition leaders. The strong rule was reflected in minor ways too, such as a ban on the sale of chewing gum, a tactic eliminating the need for gum cleanup on city sidewalks, plazas and quays, picturesque areas of commercial development along the Singapore River.
Secretary of State John Kerry said Lee transformed tiny Singapore "into one of the most prosperous and dynamic countries in the world.''
Lee led Singapore to break with British rule by merging with Malaysia in 1963. But racial tensions between Islamic Malays and Singapore's ethnic Chinese majority burst into the open with riots, and the relationship was severed in 1965, when Singapore became an independent republic.
Lee's body will lie in state at Parliament House Wednesday to Saturday for the public to pay their respects. A state funeral will be held at 2 p.m. Sunday at National University of Singapore. That will be followed by a private cremation, the prime minister announced.