"With due respect to Malaysia, I came to finish something ... you know climbing the Petronas [Towers] all the way to the top is one of my dreams and maybe because I am having the motivation, maybe also I am a little bit stubborn," Robert told Reuters news agency.
Unlike most of his ascents, there was no crowd at the base of the building to cheer him on, because the climb was done in secret aimed at avoiding detection from the authorities.
Robert was by authorities detained on the 80th floor of the tower as he was descending the building.
"We have taken him back to the police station for questioning and checking his passport. He can be charged for criminal trespass," Muhammad Sabtu Osman, the Kuala Lumpur police chief, told AFP news agency.
Robert's climb of the Petronas Towers follows two failed attempts in 2007 and 1998.
Both attempts were launched during the day, attracting attention from building security and officials who in both cases apprehended him at a deck at level 60 of the building.
Robert has scaled over 80 buildings around the world, including the Eiffel Tower, London's Canary Wharf building, New York's Empire State Building and Chicago's Sear's Tower.
In 2004, he climbed the world's tallest building, Taipei 101, in Taiwan's capital.