Battisti recently began a hunger strike to oppose his extradition
Brazil's Supreme Court has approved the extradition of former left-wing militant Cesare Battisti to Italy.
The court said Brazil's president, who granted Battisti political refugee status earlier this year, would have the final say over the extradition.
Battisti was convicted in absentia in his home country for four murders. He has denied any role in the killings.
He escaped from an Italian prison in 1981, and lived in France until fleeing to Brazil in 2004.
Brazil's Supreme Court had been deadlocked over the case, with the hearing continuing there for more than two months before Chief Justice Gilmar Mendes cast the decisive vote.
The final decision now lies with President Luiz Inacio Lula da Silva.
Correspondents say that even though it is highly unusual for Brazilian heads of state to overturn this sort of extradition ruling, it may happen in this case, given President Lula's earlier approval of political asylum for Mr Battisti.
Giving his ruling, Mr Mendes said the murders for which Battisti was convicted were "common crimes" rather than political acts.
"Certain types of crimes, even if they have political aims, cannot be considered political crimes," he was quoted as saying by AFP news agency.
"Otherwise, we could start to see cases of rape, paedophilia or torture treated as political crimes."
Italy responded rapidly to the ruling, with Foreign Minister Franco Frattini expressing his "great satisfaction".
Battisti, 54, started a hunger strike in recent days in an effort to oppose his extradition.
The murders for which he was convicted date to the 1970s, when Battisti was a member of a militant group calling itself Armed Proletarians for Communism.
He became a successful crime writer in France before fleeing when a bid to extradite him was approved.
Brazilian authorities arrested him in 2007.
President Lula's decision to grant Battisti political refugee status in January prompted Italy to recall its ambassador for "consultations".