President Tran Dai Quang welcomed Obama in front of the century-old, French colonial-style building, which stands less than 300 metres from the mausoleum of former Communist revolutionary leader Ho Chi Minh.
Schoolchildren lined the road outside the complex waving US and Vietnamese flags, as a military band played.
Obama was to participate in three meetings with senior Vietnamese leadership, including President Quang, Prime Minister Nguyen Xuan Phuc and Communist Party General Secretary Nguyen Phu Trong.
They were expected to discuss maritime security in the South China Sea, the possible lifting of a decades-old US arms embargo, and the Trans-Pacific Partnership trade deal that both countries signed in February.
The 12-nation trade pact, which excludes China, aims principally to reduce or eliminate tariffs and other non-tariff barriers.
The US president’s trip comes amidst increased Chinese assertiveness in the region, including in the South China Sea, where Vietnam and other South-East Asian countries are engaged in bitter territorial disputes with Beijing.
Obama is the third US president to visit Vietnam, following Bill Clinton in 2000 and George W Bush in 2006.
Diplomatic relations between the two countries were normalized under Clinton in 1995, two decades after the end of the US-Vietnam War.