Local police responded to pleas for help and arrested him.
The arrest this morning follows the release of CCTV vision of the brazen theft at the Aussie coffee shop Kraft Cafe where Costello was targeted by a three-person gang of thieves.
Two middle-aged men in business clothes and a blonde woman had likely scoped Costello out earlier in the day as he took photos of Aussie Olympic sailor Matt Belcher at Ipanema beach.
In two angles of the crime, the footage shows in great deal the tactics the seasoned thieves used to distract him, create the path for a quick getaway and how they tricked him into running the wrong way in pursuit of the thief.
The footage shows a woman start a conversation in Portuguese with Costello who is standing near the entrance of the coffee shop with his camera bag at his side.
As she speaks and waves her arms around, two men are seen inching towards the bag.
The first attempt to grab the bag is foiled when Brett notices his bag has moved slightly but the woman keeps talking and one of the men can be seen lifting the bag and doing a runner.
In a callous twist, the second angle shows Costello racing out of the cafe after the theft and then being pointed in the wrong direction by the second man involved in the sting.
All three thieves slip away as Costello desperately sprints up the street.