The two Vietnamese leaders sent the congratulatory messages on Friday, the Ministry of Foreign Affairs said in a press release.
National Assembly Chairman Vuong Dinh Hue also congratulated Zhao Leji on being elected as chairman of the National People's Congress Standing Committee.
Vice President Vo Thi Anh Xuan sent a congratulatory message to Han Zhengo on his election as Vice President of China.
Xi, 69, was voted as China's president for a third five-year term following an election on Friday morning, Reuters reported.
During a decade of Xi's rule, China has made many achievements in poverty reduction.
At the 20th National Congress last year, Xi outlined China's priority policies for the coming time, with an emphasis on high-quality education and innovation in economic growth.
He identified innovation as the heart of China's modernization drive, aiming to create an open and globally competitive innovation ecosystem.
In the coming working days, China's parliament is expected to elect other high-ranking positions such as prime minister, deputy prime minister, central bank governor and head of the financial agency.