"The happiness I feel today for my win is mixed with sadness for his departure," she said referring to Lula during her victory speech in Brasilia on Sunday.
"The task of succeeding him is difficult and challenging. But I know I will honour this legacy and extend his work," she said.
"I will knock on his door often, and I know it will always be open."
Rousseff pledged to eradicate poverty at home, and criticised the world's leading economies for devaluing their monies that was threatening the exports of Brazil and other countries.
A 62-year-old economist by training and a career bureaucrat, Rousseff won Lula's backing as the Workers' Party candidate against the Social Democracy Party's Jose Serra, former state governor of Sao Paulo.
Rousseff picked up 56 per cent of the vote to Serra's 44 per cent, according to an official tally of all ballots by the High Electoral Tribunal.
She will take charge on 1 January next year, when Lula, 65, is required to step down, having completed the maximum two consecutive terms permitted by law.
Rousseff has a reputation for fierce determination that Brazil's media have nicknamed her the "Iron Lady," in the mould of former British prime minister Margaret Thatcher.
She started out as a militant opposed to the 1964-1985 military dictatorship that ruled Brazil and spent three years in prison from 1970.
One of her biggest challenges is expected to be preparing the country to host the 2014 football World Cup and the 2016 Olympic Games, both awarded after Lula lobbying.
Meanwhile, Jose Serra said that his centrist opposition party would not be giving up that easily.
"To those of us imagining we're defeated: We have only started the real fight," he warned.