LIMA, Sept 28 (Reuters) - A U.S. judge on Tuesday cleared the way for former Peruvian President Alejandro Toledo to be extradited back to Peru on corruption charges, saying evidence of criminality presented in his case were "sufficient." Peruvian authorities allege that Toledo, while serving as president between 2001 and 2006, negotiated bribes with Brazilian conglomerate Odebrecht SA (ODBES.UL). Final say on whether to extradite him now lies with the U.S. State Department. Peru has been trying to extradite Toledo since 2018. Toledo has denied the graft allegations against him. He lives in California, near the Stanford University campus, where he studied and later worked. He is currently under house arrest, although he also spent several months in jail during the earlier stages of the extradition case. Toledo is one of five former Peruvian presidents whom authorities allege have engaged in corrupt acts in recent decades. Toledo and two others are alleged to have had illegal entanglements with Odebrecht. The company has admitted that its vast construction empire in Latin America also doled out bribes in many nations. Key to the decision by U.S. Magistrate Judge Thomas Hixson in San Francisco were the testimonies of Jorge Barata, the former Odebrecht head in Peru, and that of Josef Maiman, an acquaintance of Toledo who has said he helped the former president receive bribe money. "Barata and Maiman"s testimony, combined with Toledo"s admissions in this extradition proceeding that he ultimately received approximately $500,000 in Odebrecht bribe money ... establish probable cause to believe that Toledo committed collusion and money laundering," the judge wrote in his decision. Still, Judge Hixson said "the case against Toledo is not airtight," adding that witnesses had on occasion contradicted themselves, issues that would have to be resolved in a Peruvian trial. The United States extradited former Panama President Ricardo Martinelli in 2018.