Phillip Smith, 40, was arrested in a hostel in Rio de Janeiro by Brazilian police. He is expected to be extradited or deported.
Smith used a passport in his birth name, Phillip Traynor, to fly to Chile and then go to Brazil on 6 November.
He escaped while on a three-day release from a prison south of Auckland.
Smith was sentenced to life imprisonment in 1996 after he murdered the father of a 13-year-old boy he had sexually abused between 1992 and 1995.
The family had moved house but he had tracked the boy to their new home in Wellington in December 1995.
He repeatedly stabbed the father, killing him. The boy managed to escaped and raise the alarm.
The victim, who is now 30, told New Zealand's Fairfax media after news of Smith's capture, that he could now stop sleeping with a knife under his pillow.
"It's great news, it's excellent," he said from his new home in Australia. "[I feel] relief, a bit of peace of mind that I can carry on with my life without having that fear over my shoulder."
Smith's escape has thrown Corrections and various other government agencies into controversy. It has led to calls for an overhaul of short-term prison release and the monitoring of high-risk offenders.
In an email Smith sent to Radio New Zealand he said he had planned the escape by running a criminal check on his birth name and discovering that it had not been red-flagged.
"My only anxiety was that somebody that knew me might happen to be at the airport at the same time to identify me,'' he wrote, according to Radio NZ.
He also said he had been able to fund the escape with money from various businesses he had run from prison.
Smith said he chose Brazil because he thought it would be more difficult to extradite him if he was caught, as the two countries do not have a formal extradition treaty.
He was arrested after a member of the public in Rio De Janeiro recognised him from images being circulated in hostels and tipped off police. Smith appeared in court after his arrest and has been remanded in custody for 60 days.
New Zealand Police Detective Superintendent Mike Pannett said in a press conference on Thursday that it was a relief to have Smith back in custody.
He would not, however, say how long he expected Smith to remain in Brazil.
"New Zealand will bring him back as soon as possible but we are reliant on the Brazilian justice system to process and deal with the situation," Mr Pannett said.
Criminal Bar Association President Tony Bouchier said police needed to be more thorough when checking the names of criminals.
"There's got to be a far more robust process gone through when police are entering people's names into their systems and starting somebody off with a criminal record," he told Radio NZ.
Corrections Minister Peseta Sam Lotu-Iiga urged a review of the incident "so we can make some decisions as to how we can improve how we have temporary releases done out in the community", according to Radio New Zealand.

James Johnston & Co of Elgin said turnover rose from £58.6m in 2014 to £66.6m last year.
Operating profit rose from £2.27m to £8m, supported by an exceptional gain of £4.1m on the sale of a property in London.
The firm said sales growth was generated by increased sales to luxury brands in the UK and France.
It also benefited from growth in sales of its own branded products through its UK retail outlets, while wholesale gains were driven by Japan and the Middle East.
The company has manufacturing plants in Elgin and Hawick. It runs several shops in the UK, including a flagship store in New Bond Street, London, which opened in December last year.
In 2015, it employed an average of 943 employees - up from 829 in 2014.
A New Zealand man serving a life sentence for child molestation and murder who escaped to Brazil is now in custody, New Zealand police say.
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The company behind Scottish cashmere brand Johnstons of Elgin has reported a sharp rise in sales and profits.