They said Battisti was tracked down via a young woman from his support committee who was under surveillance.
The woman was to meet Battisti to give him money. Italian police had been tipped off to the plan, the police officials said.
Clemente Mastella, Italy's justice minister, congratulated police in Italy, France and Brazil for the "brilliant operation", the Ansa and Apcom agencies said.
He said he hoped Battisti could quickly be extradited to Italy. Battisti had been living in France for years and established himself as a writer of police thrillers.
Like dozens of other Italians, he profited from a French policy of allowing militant leftists allegedly responsible for bombings and murders in Italy in the 1970s and '80s to take refuge in France if they renounced their violent ways.
However, France signed an extradition order in 2004 for Battisti that sent him back into hiding.
A former member of the Armed Proletarians for Communism, Battisti was convicted in absentia and sentenced to life in prison in Italy in 1990 for the murders of a prison guard and a butcher in the late 1970s.
The conviction was confirmed by Italy's high court in 1993.
Battisti is accused of being an accomplice to two other murders, including the killing of a police officer.
He escaped from an Italian prison in 1981 and took refuge in France in the early 1990s.
He has denied killing anyone and reiterated his claim of innocence in a book published in France a year ago.
He wrote in Ma Cavale (My Escape): "I am guilty, as I have often said, of having participated in an armed group with a subversive aim and of having carried weapons. But I never shot anyone."