At a reception held by President Vo Van Thuong at the Presidential Palace, the leaders also participated in a flag salutation ceremony and Widodo received a guard of honor.
The two leaders then held discussions on bilateral relations and witnesses the signing of several agreements.
Widodo is on a state visit to Vietnam from Thursday to Saturday, and is expected to participate in a number of events in Hanoi.
The two leaders are also expected to discuss measures and directions for cooperation in several fields like the economy, commerce, investment, security, defense, transport, and agriculture.
Vietnam and Indonesia, who established diplomatic relations in 1955, upgraded them to a comprehensive partnership in 2003 and strategic partnership in 2013.
Vietnam is Indonesia's sole strategic partner in ASEAN.
Indonesia is Vietnam's third largest trade partner in Southeast Asia, while Vietnam is Indonesia's fourth largest.
In the first 11 months of last year bilateral trade was worth US$12.6 billion.