Michel Fourniret, dubbed the Ogre of the Ardennes when he was jailed for life for the killing of seven girls in 2008, recently admitted to magistrates in Paris that he had killed 20-year-old Joanna Parrish and French teenager Marie-Angèle Domece, lawyer Didier Seban told the AFP news agency.
"He made detailed and repeated confessions. He clearly recognises, and this several times over, having killed Joanna Parrish and Marie-Angèle Domece," Seban said. "It's a new development, a resolution of the affair, it seems, in a remarkable way.
"It's hard [for the family] but the end of a long legal battle."
He said he hoped there would soon be a new trial.
Parrish had been working as a language assistant at a secondary school in Auxerre, in the Burgundy region.
He body was found in May 1990 and an autopsy found she had been raped and beaten.
Domece disappeared in July 1988 and her body has never been located.
Fourniret was charged with kidnapping and murdering the two girls in 2008 but an appeals court dismissed the case in 2011.
His wife, Monique Olivier, twice accused him of the two unsolved murders but later retracted.
"Monique Olivier will in turn have to be questioned," Seban added.
Until now Fourniret has denied involvement in the two cases.
Olivier was found guilty of complicity in five murders and jailed for life with an order that she serve at least 28 years behind bars.
In June 2012 the court of appeal in Paris cancelled the dismissal order on Fourniret and asked for investigations to resume based on new leads.