Wong, 51, comes from among a crop of so-called "4G" leaders, a new generation of politicians hand-picked by the long-ruling People's Action Party (PAP) to take over the reins of the key Asian trade and financial centre.
He is the first Singaporean leader born after its independence in 1965.
Wong will retain his current position as finance minister and takes charge of a country led for two decades by Lee Hsien Loong, the 72-year-old son of Lee Kuan Yew, the founder of modern Singapore who stayed in politics until his death in 2015.
The succession has been long coming, with Lee's plans of stepping down before he turned 70 up-ended by the pandemic, and by a transition fumble when his anointed successor unexpectedly ruled himself out of the running in 2021.
Wong has pledged to lead "with humility and a deep sense of duty" towards Singapore and its 5.9 million people and devote "every ounce of my energy" to the people.
Wong rose to prominence in 2020 as co-chair of the pandemic task force and was named Lee's successor in April 2022 after a series of consultations between the political leadership and Wong's peers.
He was promoted to deputy prime minister and led a high-profile public consultation exercise to chart a "social compact" between the government and the people on dealing with issues like sustainability, inequality and employment.
Wong made a very minor cabinet reshuffle on Monday, promoting the trade minister to become his deputy, noting that continuity and stability were key considerations. He has pledged a bigger reshuffle after an election due by 2025.
Lee will remain in Wong's cabinet as senior minister, as former Singapore prime ministers have done, preserving the political clout of the long-serving Lee family.
His father stepped down as leader in 1990 and stayed on in the cabinets of his successors for 21 years, initially as senior minister then as "minister mentor" in his son's government.
In his final major speech on May 1, Lee urged people to rally behind Wong and emphasised that Singapore's stable politics had enabled long-term planning.
"I feel a sense of satisfaction and completeness," an emotional Lee told the crowd.
Opposition leader Pritam Singh said on Wednesday Wong was taking over at a challenging time with an uncertain and more unpredictable external environment, and significant generational shifts on the domestic front.
"Under Prime Minister Wong's leadership, the Workers' Party will continue to play our legislative role to advance the interests of Singapore and Singaporeans," said Singh.
