Oviedo's supporters targeted Congress last year
The decision opens the way for the retired general's extradition on charges relating to the murder of Paraguay's former vice-president.
General Oviedo, who also led a failed coup attempt in 1996, has been under house arrest in Brazil's capital, Brasilia, since his capture last year.
His lawyers argued he would face political persecution if sent back to Paraguay.
But Brazil's National Refugee Commission turned down his request for asylum.
Brazil's Supreme Court must now decide if the extradition goes ahead.
Paraguay's government, made up now of General Oviedo's political opponents, wants him to stand trial on charges that he masterminded the 1999 assassination of Vice-President Luis Maria Argana.
General Oviedo was the main powerbroker in the long-ruling Colorado Party and considered more influential than then-President Raul Cubas.
Mr Argana's killing sparked a political crisis, and General Oviedo fled to Argentina where he was given political asylum.
But it became clear he was still pulling strings at home and his asylum was revoked.
Wigs and mobile phones
For several months, he was on the run, and regularly called in to Paraguayan radio stations to denounce the government.
When he was eventually caught by the Brazilian police, he was discovered with 10 mobile phones and a collection of wigs that he used to conceal his identity.
General Oviedo has already been sentenced in Paraguay to 10 years jail for his role in the failed coup attempt. He has also been accused of inciting last year's revolt in a Paraguayan military barracks, which was suppressed.
He is now under house arrest in Brasilia in the same neighbourhood as former Paraguayan President Alfredo Stroessner, who Brazil did grant asylum to.