Following the funeral, Giap's body was flown to his home province of Quang Binh in central Vietnam, with hundreds of thousands of people lining the 70-kilometer (43-mile) route from the airport to his burial site.
The burial ceremony was attended by President Truong Tan Sang and other top officials and broadcast live on state television.
Giap was buried in Quang Binh instead of the Mai Dich cemetery in Hanoi, where most high-ranking Vietnamese officials are traditionally buried, in accordance with his and his family's wishes.
Giap is best remembered for leading Vietnamese forces to victory over the French at Dien Bien Phu in 1954.
His Chinese advisers told him to strike elite French forces fast and hard, but Giap changed plans at the last minute and ordered his jungle troops, clad in sandals made of old car tires, to besiege the French army. The French were defeated after 56 days, and the unlikely victory led not only to Vietnam's independence, but hastened the collapse of colonialism across Indochina and beyond.
Throughout most of the war that followed against the United States, Giap was defense minister and armed forces commander, but he was slowly pushed aside after Ho Chi Minh's death in 1969. The glory for victory in 1975 didn't go to Giap.
"No words can describe how much love and respect people reserve for Gen. Giap," 71-year-old Nguyen Thi Vi, from the central province of Ha Tinh, said as she waited in the crowd in Hanoi to pay her final respects.
"I feel like I lost one of my relatives," she said. "Gen. Giap will live forever in the heart of Vietnamese people and we may not witness another great man like him. We should set up temples to honor him and where people can go and pay their respect."