Mr Robert, 47, scaled the 88-storey Tower 2, triumphantly unfurling a Malaysian flag as he stood on its 1,483ft pinnacle (452m) on the country's national day.
He took just over two hours to reach the top after setting off in darkness before dawn to avoid the security that had thwarted his previous bids.
But when he came down to the 80-floor viewing deck shortly after 7.30am he was apprehended by security and arrested.
Mr Robert is being held by police in Kuala Lumpur. He has not been charged but is being investigated for criminal trespass, which carries a maximum jail term of up to six months and a £521 fine.
"With due respect to Malaysia, I came to finish something," Mr Robert told Reuters before setting off. "You know, climbing the Petronas [Towers] all the way to the top is one of my dreams, maybe because I am having the motivation, maybe also I am a little bit stubborn." On his two previous attempts in 1998 and 2007 Mr Robert was seized by security guards when he reached the twin Petronas Towers' sixtieth floor, prompting secrecy this time.
It meant there were few spectators to witness his feat, though it was captured on video by a cameraman, Ee Wee Kiat, who was tipped off.
"He climbed using his bare hands and reached the top very fast as no security personnel noticed him or stopped him," said he cameraman.
The climber has scaled more than 80 tall buildings around the world, including London's Canary Wharf building, Paris Eiffel Tower, and New York's Empire State Building, always without ropes and has suffered several falls resulting in serious fractures.source
