Lee, son of Lee Kuan Yew, is only the third prime minister since the island city-state won independence from Britain in 1965.
After taking the oath, the 52-year-old immediately began to look ahead to future leaders.
"The next generation of leaders must come from the post-independence generation. Hence leadership succession will be one of my top priorities," he said, the Voice of America reported.
Under his predecessors, Goh Chok Tong and Lee Kuan Yew, Singaporeans achieved a level of prosperity that other Asians could only dream about, he said.
But now many of the country's youth are aspiring for less tangible goals, such as greater freedom to express themselves and a more clearly defined culture.
Lee also referred to the U.S.-led war on terror, saying it could destabilize race relations in Singapore.