Mr Lee was admitted to Singapore General Hospital on February 5 for severe pneumonia and was later put on life support.
Singapore's Prime Minister's Office said in a statement on its website that Lee "passed away peacefully".
New Zealand Prime Minister John Key today expressed his sincere condolences.
"Mr Lee made an extraordinary contribution to Singapore, both as it found its way to independence in 1965 and in the 50 years since then," he said.
"A man of rare qualities, Mr Lee's courage, determination, commitment, character and ability made him a formidable leader who held the respect of Singaporeans and the international community alike."
He guided Singapore for 31 years until 1990, making it into a global trade and finance center.
He has faced criticism, though, for using tough tactics to consolidate power.
Mr Lee jailed some political rivals without trial for decades and brought defamation lawsuits against journalists and opposition politicians.
Mr Lee commanded immense respect among Singaporeans, who this year will celebrate the country's 50th independence anniversary.
Singapore's Prime Minister's Office said arrangements for the public to pay respects and funeral arrangements will be announced later.
