Workers removed windows from the glass-faced, 58-storey skyscraper to prevent him from going higher.
Police officers eventually grabbed the man as he reached the 21st floor and pulled him inside the building.
The building is the headquarters of the US presidential campaign of Republican nominee Donald Trump. He also lives in the building but was not in New York.
Police described the climber as a 20-year-old man from Virginia who wanted to meet Mr Trump. Police said they did not believe the man intended to harm anyone.
In a YouTube video posted earlier this week he described himself as an "independent researcher" and needed to deliver an "important message" to Mr Trump.
The man was taken to Bellevue Hospital to be psychologically evaluated, police said.
Large crowds gathered outside the building along Fifth Avenue as the incident unfolded over several hours.
"This man performed a ridiculous and dangerous stunt," said Michael Cohen, executive vice-president of the Trump Organization. "I'm 100% certain the NYPD had better things to do."
New York police have arrested a man who tried to scale Trump Tower in midtown Manhattan using rope and suction cups.