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.
More on this and other Staffordshire stories
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.

Hewlett died at the age of 58 last month, having shared his experience of coping with cancer on BBC Radio 4.
He was told of the honour in January, saying he was "touched" by the accolade. Awards chair Stewart Purvis said he had "achieved so much".
A scholarship has been launched in his name to help students from lower income families studying broadcast journalism.
One recipient each year will be presented with the Steve Hewlett Scholarship, which has been set up by the RTS and The Media Society. As well as a financial contribution to their studies, the recipient will be mentored by RTS members and former colleagues of Hewlett.
Hewlett's sons collected the judges' award on his behalf.
The Media Show presenter and Guardian journalist married his partner Rachel Crellin earlier in February, after being told he did not have long to live.
Hewlett had spoken movingly about his cancer journey on the PM programme with Eddie Mair, who announced his death on the show on 20 February.
Purvis said: "The panel chose a winner who achieved so much on screen and off screen, over the course of his career and very particularly in the past year.
"I phoned the winner and that's how I got to tell Steve Hewlett that he had won the judges' award. Steve told me he was honoured and touched to have won. He looked forward to receiving it on 1 March.
"I don't think there has ever been anybody in broadcasting quite like Steve Hewlett. And probably never will be again."
RTS Television Journalism Awards winners
Full list of winners
Two of the awards went to Syrian film-maker Waad al-Kateab, who was granted a visa by the Foreign Office to travel to the UK after leaving her home country.
She won the young talent of the year award and was named camera operator of the year, the first time that award has been given to a woman.
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A child rapist who fled the UK has been arrested in Brazil after three years on the run.
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Broadcaster Steve Hewlett has posthumously been given a top honour at the Royal Television Society awards.