Brazil's Supreme Electoral Court declared Lula the next president, with 50.9% of votes versus 49.1% for Bolsonaro.
Bolsonaro did not make a call to Lula, according to campaign advisers.
"I will govern for 215 million Brazilians, and not just for those who voted for me," Lula said at his campaign headquarters.
Lula arrived at a rally in Sao Paulo shortly after 8:00 p.m. (1100 GMT), waving from the sunroof of a car.
A senior Bolsonaro campaign aide, speaking on condition of anonymity, said he would not make a speech on Sunday.
A former union leader born into poverty, Lula organized strikes against Brazil's military government in the 1970s.
In his third term, Lula will confront a sluggish economy, tighter budget constraints and a more hostile legislature. »