Lula, a former union leader, won about 61 per cent of the vote against 39 per cent for Alckmin of the centrist Brazilian Social Democracy party, according to official results.
Voters appeared to have overlooked a series of corruption scandals and repaid Lula for helping the poor and workers.
About 125 million Brazilians on Sunday cast ballots across the world's fourth-largest democracy, from hamlets in the Amazon rainforest to slums in the big cities.
In a victory address, the bearded Lula promised to take care of the poor people whose support helped carry him to a re-election. He promised to govern Brazil for everyone, but said: "The poor will have preference in our government."
Jubilant Lula supporters, many wearing red T-shirts, flocked to Sao Paulo's main business thoroughfare, Avenida Paulista, to celebrate waving Workers party flags. Bands blared out dance music from trailers stacked with walls of speakers.
"Lula is not indebted to the rich. He owes his success to the common Brazilian"
Euler Peixoto, Sao Paulo voter
Lula said: "The people felt that their lives have got better. There is no contest to this. Because the people felt it on their plates, on the table, in their pockets."
Lula fell shy of an absolute majority in an October 1 vote against a wider field after an attempted smear campaign by his Workers' party against opposition candidates backfired.
Support from the lower classes, who have benefited from more jobs as well as welfare programmes during his four-year term, seem to be the key to Lula's comeback.
Euler Peixoto, 48, a photographer who voted in a middle-class district of the business capital, Sao Paulo, said: "I want someone like that as my president. Lula is not indebted to the rich. He owes his success to the common Brazilian."
Scandals over vote-buying and bribery in the past few years had threatened to torpedo Lula's political career, and they still weighed on many minds, especially among the rich and better-educated Brazilians.
Voters said violent crime, education and health costs were all vital issues.
Lourdes Oliveira, a 34-year-old nurse in the Rocinha shantytown in Rio de Janeiro, said: "Here, violence is the biggest problem. I believe Lula when he says only education can take youngsters away from the streets and from drug-trafficking."