He will meet several Vietnamese leaders during the four-day visit, which will reaffirm Singapore's longstanding ties with Vietnam.
They will discuss ways to strengthen bilateral cooperation that is underpinned by the Strategic Partnership concluded during Mr Lee's last official visit to Vietnam in September 2013, the statement added.
Mr Lee will be in Ho Chi Minh City on March 21 and 22, and Hanoi from March 22 to March 24.
In Hanoi, he will call on Communist Party of Vietnam General Secretary Nguyen Phu Trong and Vietnam President Tran Dai Quang.
He will also meet his Vietnamese counterpart, Prime Minister Nguyen Xuan Phuc, as well as National Assembly President Nguyen Thi Kim Ngan.
Mr Lee will be given a welcome ceremony at the Presidential Palace and will be hosted to an official dinner by Mr Phuc.
He will also lay wreaths at the Ho Chi Minh Mausoleum and the Monument of National Heroes and Martyrs.
On Friday, Secretary of Da Nang City Party Committee Nguyen Xuan Anh and Chairman of Hanoi People's Committee Nguyen Duc Chung will both call on Mr Lee.
While in Ho Chi Minh City, Mr Lee will officiate the opening of the Mapletree Business Centre and attend a luncheon with businessmen based in the city. He will also meet Singaporeans staying in Ho Chi Minh City.
Singapore is the third largest foreign investor in Vietnam with investments of US$37.9 billion (S$53 billion) in 1,786 projects. Bilateral trade with Vietnam stood at S$19.8 billion last year.
Singapore is also the top foreign investor in Ho Chi Minh City - with investments of US$10.2 billion (S$14.3 billion) in 937 projects, largely focused in the real estate sector.
Mr Lee will be accompanied on the visit by Mrs Lee, Minister in the Prime Minister's Office Chan Chun Sing, Senior Minister of State for Foreign Affairs and Defence Maliki Osman, Parliamentary Secretary for Culture, Community and Youth Baey Yam Keng and Member of Parliament Intan Azura Mokhtar. The delegation will also include senior officials from the Prime Minister's Office and the Ministry of Foreign Affairs.
Deputy Prime Minister Teo Chee Hean will be Acting Prime Minister in Mr Lee's absence.