Lee passed away peacefully at Singapore General Hospital at 3:18 a.m., the statement said.
He had been in the hospital with pneumonia since February 5.
Born in 1923, Lee co-founded the city state in 1965 when it declared its independence from Malaysia and was its prime minister for more than three decades.
"The first of our founding fathers is no more," Prime Minister Lee Hsien Loong, who is Lee's son, told the nation in a televised speech Monday.
"He fought for our independence, built a nation where there was none and made us proud to be Singaporeans," Lee said.
Building up Singapore was his passion, the Prime Minister said, reading out a quote from his father: "At the end of the day what have I got? A successful Singapore. What have I given up? My life."
Lee's body will lie in state at Parliament House from Wednesday through Saturday. A state funeral will be held Sunday.
UN Secretary General Ban Ki-moon issued a condolence statement and said Lee "helped Singapore to transition from a developing country to one of the most developed in the world, transforming it into a thriving international business hub."
President Obama called Lee a visionary who helped him formulate U.S. policy of "rebalancing to the Asia Pacific," when the two met in Singapore in 2009.
"He was a true giant of history who will be remembered for generations to come as the father of modern Singapore and as one the great strategists of Asian affairs," the President said.
U.S. Secretary of State John Kerry also praised the advice he got from Lee, calling it "the most valuable and insightful I have received."
"He was, of course, a uniquely astute analyst and observer of Asia, and it is largely through his life's work that Singapore became one of the United States' strongest strategic partners in the region," Kerry said.
Former President George H. W. Bush said he respected Lee's effective leadership of a "wonderful, resilient and innovative country in ways that lifted living standards without indulging a culture of corruption."
He added, " Because of the example set by Lee Kuan Yew's singular leadership, I am confident that the future will be bright for Singapore."
China's foreign ministry called Lee "a uniquely influential Asian statesman," and Australia's Prime Minister Tony Abbott said "our region owes much to Lee Kuan Yew."
Japan's Prime Minister Shinzo Abe and Indonesia's foreign ministry also praised Lee's leadership in their condolence notices.
Singapore's President Tony Tan Keng Yam called Lee the "architect of our modern Republic," in a letter to Lee's son, the current prime minister.
"Few have demonstrated such complete commitment to a cause greater than themselves," President Tan said.