The casket containing Etienne Tshisekedi’s body remained in the stadium overnight.
After the funeral ceremony, Etienne Tshisekedi will be buried at his private N’sele residence, some 40km (25 miles) east of central Kinshasa.
He died aged 84 in Brussels and his body was kept in a funeral parlour until it could be returned home.
On Friday afternoon, the Martyrs’ Stadium in Kinshasa erupted in cheers as the casket containing Tshisekedi’s remains entered, reports the BBC’s Gaius Kowene.
His supporters screamed and blew whistles in the 80,000-capacity arena.
The campaign to bury Tshisekedi’s remains in his home country faced obstacles from President Félix Tshisekedi’s predecessor, Joseph Kabila.
For his supporters, Tshisekedi coming home represents a victory over the former government, our correspondent says.
A life of opposition
Tshisekedi spent decades in politics but failed in several attempts to become president.
He served as interior minister under the country’s authoritarian leader Mobutu Sese Seko, before joining the political opposition.
After serving time in prison, he founded the Union for Democracy and Social Progress (UDPS) in 1982 and was appointed prime minister by Mobutu, though the two frequently clashed.
In 1997, Mobutu was ousted as leader in a rebellion led by Joseph Kabila’s father, Laurent.
Tshisekedi became an opponent of the new regime, and of Joseph Kabila after Laurent Kabila was assassinated in 2001.
He boycotted DR Congo’s elections in 2006, alleging vote fraud, and was beaten in a 2011 race marked by allegations of widespread voting irregularities.
Félix Tshisekedi won a bitterly contested election last year. It marked the first peaceful transition of power since DR Congo gained independence from Belgium in 1960.
However, several observer groups believe that another opposition candidate, Martin Fayulu, was the rightful winner.
Since coming to power, President Tshisekedi has agreed to work with the party of former President Joseph Kabila.