Boko Haram kidnapped German citizen Robert Nitsch Eberhard in Nigeria in July, Biya said in a statement read Wednesday on state-run broadcaster CRTV. He did not detail how, when or where the rescue operation took place.
"A special operation of Cameroonian armed forces and security services of friendly countries" freed the man, he said.
Eberhard told journalists he was glad to be alive.
"I am happy to see all these people around me, who have rescued me and made sure that I survived, because until the last minute, I did not know whether I would survive or I would not survive. It was for me a big problem. Because it was darkness, total darkness, and you see nobody around you. Then this is a big problem to say OK, I will survive or not survive," Eberhard said.
Eberhard was flown in from Cameroon's Far North Region to Yaounde shortly after noon Wednesday.
He said he was grateful to all those who worked to secure his release.
The German ambassador to Cameroon, Klaus-Ludwig Keferstein, also thanked Cameroonian authorities, particularly because "we could find a solution to this problem of hostage-taking," he said.
Eberhard spoke amid heavy security and mentioned that he was teaching at a vocational school in Gombe, Adamawa state, Nigeria, before the insurgents took him hostage in July.
He has been taken to the residence of the German ambassador in Yaounde. The ambassador said initial medical care will be given to him before he is flown back to Germany for more medical attention.
Biya said he was thankful to all those who "directly or indirectly helped in the achievement ... and particularly the German government for their precious contribution."
He did not specify how Germany participated. The German Foreign Office did not immediately respond to CNN's request for comment.
Nkosazana Dlamini-Zuma, chairwoman of the African Union Commission, praised "the decision of President Idriss Deby Itno of Chad, at the request of Cameroon, to deploy troops in that country, to contribute to the ongoing operations against the Boko Haram terrorist group."
Islamist group has terrorized northern Nigeria
Boko Haram, which has fought an anti-government campaign in northeastern Nigeria and parts of Cameroon, said previously that it was holding a German hostage.
Boko Haram leader Abubakar Shekau said so in November, in a video message denying Nigeria's claims that it had struck a ceasefire deal with the group. It wasn't immediately clear if this was Eberhard.
The operation came days after about 2,000 Chadian troops arrived in Cameroon to help fight the insurgents.
Boko Haram, which means "Western education is forbidden" in the local Hausa dialect, has terrorized northern Nigeria regularly since 2009, attacking police, schools, churches and civilians, and bombing government buildings. It has kidnapped students, including more than 200 schoolgirls who were abducted in northeastern Nigeria in April and remain missing.
The Islamist group has attacked neighboring Cameroon, initially by crossing the border from Nigeria to steal food or kidnap foreign nationals. More recently, the group went after Cameroonian military installations.
On Sunday, suspected Boko Haram militants kidnapped 80 people in Cameroon's Far North Region, officials in the country said. By Monday, a military operation had freed 24 of the captives; three others were found dead, state-run media reported.
Boko Haram has said its aim is to impose a stricter form of Sharia law across Nigeria, which is split between a majority Muslim north and a mostly Christian south.
Biya has called for international cooperation in the fight against Boko Haram. Last week, the Russian ambassador to Cameroon, Nicolay Ratsiborinski, said his country will supply Cameroon with modern and sophisticated military weapons, including heavy artillery, armored cars and missiles.
Michael Stephen Hoza, U.S. ambassador to Cameroon, said the United States would help train Cameroon soldiers and offer equipment for the fight.