Portuguese national Antonio Pedro De Olivera Alves, 44, was convicted in his absence at Stafford Crown Court of raping the 12-year-old girl.
He was sentenced to an 11-year jail term in 2013, and a warrant for his arrest was issued.
Alves, who was arrested in South America earlier this month, will face extradition proceedings, police said.
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Prior to raping the girl, Alves befriended her by posing as a teenager.
He was charged in January 2013 and convicted in June the same year.
Staffordshire Police worked with the UK National Crime Agency and Brazilian authorities to catch Alves, who was arrested earlier this month.
He will remain in custody until the Brazil High Court rules on his expected extradition to the UK, said police.
At the time of arrest, Alves lived at Aneurin Bevan Place in Rugeley and worked in Stafford.
A child rapist who fled the UK has been arrested in Brazil after three years on the run.