Speaking to his Vietnamese counterpart Lt. Gen. Do Ba Ty before the closed-door talks, Gen Dempsey described his visit, the first to communist Vietnam by a American chairman of the joint chiefs of staff since 1971 when the Vietnam War was on, as "one of the highlights" of his military career.
The sides will work to boost their military cooperation, with a focus on maritime security, training, and overcoming the consequences of the war, a Vietnamese Ministry of Defence statement said.
During his four-day stay, Gen Dempsey will have talks with Prime Minister Nguyen Tan Dung and Defence Minister Phung Quang Thanh. He is expected to visit a former US air base in Danang in central Vietnam, where the US two years ago began a landmark project to clean up Agent Orange from the site.
Part of the former base consists of a dry field where US troops once stored and mixed the defoliant before it was loaded onto planes to be sprayed to deny forest cover for the communist fighters during the war.
Bilateral trade and investment relations have grown quickly since the normalization of relations in 1995, making the US one of Vietnam's top trading partners and investors, but military cooperation has been limited because of a US ban on lethal arms sales to Vietnam.
The US has indicated that it may partially lift the ban as early as next month, saying Vietnam progressed on human rights.
Closer military ties between Vietnam and the United States may anger China, which has been more assertive recently on maritime claims that overlap with claims by Vietnam.
Russia is Vietnam's main source of armaments, and Hanoi has earmarked hundreds of millions of dollars to build more vessels to improve its maritime capability.