Military trucks carrying Giap's flag-draped coffin were met by vast crowds - at places 10 or 20 deep - with many mourners crying, chanting or praying in Vietnam's biggest state funeral in decades.
Giap was the architect of Vietnam's stunning battlefield victories over France and the United States and the one-party communist state has keenly tried to co-opt the popular general's legacy to bolster its own legitimacy.
"(Giap) is the general of the People and his name will be forever engraved in the history of the nation," Communist Party leader Nguyen Phu Trong said in a televised speech.
Giap, who became a prominent government critic late in life, is second only to founding president Ho Chi Minh in the communist nation's affections.
"The general will live forever!" one man shouted as the funeral procession drove by to the airport, where his body will be flown to his native Quang Binh province some 500 kilometres away for burial later today.
Hundreds of thousands of people have flocked to pay their last respects to Giap, lauded as a military genius for the guerrilla tactics that inspired resistance movements around the world, since he died last week at 102.
"He's gone, taking with him part of our glorious victory," said retired civil servant Tran Hung Tuy, 74.
"People admire and love Giap from the bottom of their heart," he told AFP after he finished a prayer as the coffin went past.
The enormous crowds are highly unusual in authoritarian Vietnam, which heavily stage-manages anniversary events and routinely breaks up political protests with force.
General Giap is survived by Dang Bich Ha, his wife since 1949, and four children.