Lula, who turns 81 on Tuesday, has already been president for three non-consecutive terms, serving two terms between January 2003 to December 2010, and again from January 2023.
His win makes him the first in Brazilian history to secure a fourth term, which will last until 2030.
But this has been a bitterly fought campaign and the new term - set to start on 5 January - comes amid significant constraints at home and abroad, including animosity from US President Donald Trump.
Referring to what Trump has called the "Donroe Doctrine" - which seeks to establish US dominance in the Western Hemisphere - Lula used his victory speech to insist that Brazil "will not accept being anyone's backyard".
Trump has previously shown support for Bolsonaro's father Jair, who is currently serving a 27-year prison sentence after being convicted of a coup attempt after losing the 2022 elections to Lula. Flávio Bolsonaro met Trump at the White House earlier this year to bid for his support.
Lula has also bucked a wider trend in Latin America, where voters in countries such as Argentina, Chile and Colombia have put right-wing candidates and parties in power.
While Trump has yet to react, other world leaders have been congratulating Lula on his win.
Ecuador President Daniel Noboa Azin said the region had "common enemies, shared challenges, and much to gain when we work together."
European Commission President Ursula von der Leyen said "democracy and multilateralism" had won. Spanish Prime Minister Pedro Sánchez - also a left-wing leader - called it a "great victory", saying "the comeback of global progressivism has just begun". French President Emmanuel Macron said the two nations should work "in service of a more just world".
South African President Cyril Ramaphosa called Lula's victory one for the "global south and progressive forces throughout the world".
Additional reporting by Vinícius de S. Mendes, BBC Brasil
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