The climber was on the East 56th Street side, the south side of the 58-story building. A witness said the man was standing on the sub roof garden, which is accessible to the public, when he started his climb.
He used several suction cups to scale the building, climbing as high as the 21st floor.
The man was wearing a backpack and had leaflets, according to New York police.
Police and firefighters responded to the scene and attempted to apprehend the man for more than two hours as he played a cat-and-mouse game. Authorities said the incident appeared to be a stunt.
Emergency Services workers cut holes into grates in the building, as possible places to intercept the climber. When that proved ineffective, they started breaking a window and lowering a window washer scaffolding down the building toward the man.
PHOTOS: Man climbs Trump Tower in NYC with suction cups
Eventually crews used the scaffolding and removed two windows, trapping the climber. He was taken into custody at about 6:30 p.m. local time.
Police set up barricades around the area as a precaution and also placed out large inflatable cushions.
Officials said they didn't want to take any actions that could have caused the climber to fall. According to police, the man didn't appear to have any type of weapon in his backpack.
Police said the 20-year-old man from Virginia posted a video to YouTube on Tuesday at about 5:40 p.m. appealing to Trump to finance a research grant for him.
In the video, the climber said he wished to have a personal meeting with trump and also urged people to vote for the Republican presidential nominee.
According to authorities, the man traveled to New York City on Tuesday and was staying at a hotel. He was taken to the hospital for a psychological evaluation, police stated.
The building is headquarters to Trump's presidential campaign and he also lives there.
Trump was not in the building at the time of the incident, as he was campaigning in Virginia in the afternoon and headed to Florida for an evening event.
Officials said the Secret Service was consulted, but there didn't appear to be any harm directed at Trump. Police said the climber never expressed wanting to impose any harm on anyone.
Police stated the climber would face charges such as reckless endangerment, criminal trespass and more.