Lee, 72, had previously said the succession would take place by November 21 this year, the 70th anniversary of the ruling People's Action Party (PAP).
After the handover, Wong, 51, will lead the PAP into the next general election, due by November 2025.
The city-state has had three prime ministers since its 1965 independence, all serving relatively long terms. Lee Hsien Loong, son of first Prime Minister Lee Kuan Yew, took office in 2004.
Lee had said he originally planned to step down as prime minister in favor of the leader of the PAP's "fourth generation" or "4G" team by 2022, before he turned 70. But that plan was "disrupted" by the COVID-19 pandemic, he said.
In April 2022, Wong was endorsed as the 4G leader. Since then, Wong, who doubles as finance minister, has been shepherding key policies and foreign diplomac