The appointment was approved by the National People's Congress, the Xinhua News Agency reported.
The appointments of Xi and Li completed the once-in-a-decade leadership change in the Communist country.
Li, who was born in Anhui province, joined the Communist Party in 1976 after graduating from Peking University with degrees in economics and law. He was appointed vice premier in 2008 and was re-elected in November to the powerful Politburo Standing Committee.
As premier, Li must tackle a large portfolio of domestic affairs, economic challenges, environmental woes and China's urbanization drive, the BBC said.
U.S. Secretary of State John Kerry and Treasury Secretary Jack Lew have planned visits to Beijing as the new Chinese administration takes over.