Whelan gave himself up to the Rio de Janeiro-state Justice Tribunal in downtown Rio and would be picked up by police, the court said.
Rio state prosecutors have accused 12 people of engaging in criminal organisation, bribery, money-laundering and tax evasion in connection with a World Cup ticket "scalping" ring.
Scalping, or reselling tickets for profit, is illegal in Brazil.
Briton Whelan is chief executive of MATCH Services which had been granted the exclusive right to sell VIP tickets for the World Cup from FIFA, the world soccer governing body.
MATCH is the main provider of hospitality packages for the World Cup and paid $240 million for the exclusive rights to sell corporate hospitality at the 2010 World Cup and this one.
In a statement, MATCH said all sales followed FIFA's procedures, denied Whelan participated in any illegal scheme to resell tickets and vowed to collaborate with the Brazilian police.
"We are confident that the investigations carried out by the Brazilian authorities will bring more transparency to the facts and will clear MATCH's staff and show the probity of its work," the company said in the statement.
A judge approved detention for 11, including Whelan, on June 10. Police allege that Whelan fled the Copacabana Palace hotel shortly before they arrived to detain him.
Shortly after the failed arrest, Whelan was declared a fugitive and his name was placed on an international Interpol watch list.
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