Brazil's Supreme Court ruled last year that Battisti should be extradited on murder convictions from the 1970s in Italy, but left the final decision to Mr Lula.
The move, announced in a statement yesterday, comes a day after Italian premier Silvio Berlusconi warned that such a decision would be "incomprehensible and unacceptable."
Battisti denies the murders and says he is being persecuted in Italy. He faces life in prison for the murders in the 1970s, a violent period known as the "Years of Lead," when he belonged to a guerrilla group called the Armed Proletarians for Communism.
Mr Lula, who ends his second term in office on Saturday, had granted Battisti refugee status in January 2009, straining ties with Italy. The pending decision has been one of the main issues during the final days of Mr Lula's presidency.
Battisti escaped from an Italian prison in 1981 and lived in France, but fled when Paris approved his extradition in 2006.
He was arrested while on the run in Brazil.