The man, who was not immediately identified, "is in the hands of the emergency teams" deployed to the tower, which will reopen to visitors as normal early on Tuesday, the company operating the structure said in a statement.
It said firemen who had rappelled down from the tower's third-floor observation deck to near the black-clad climber managed to "talk the individual down".
The man "has been grabbed," a police official added.
Emergency procedures triggered by the man's unauthorised climb forced an evacuation of the iconic monument, the esplanade underneath it and a large section of the adjacent Champ de Mars park mid-afternoon Monday.
The abrupt closure of one of France's biggest tourist draws frustrated visitors who had been planning to go up the 324-metre (1,063-foot) tower.
"We're really disappointed, we're only here for a week and this messes with our whole programme," said Sylvie and Celine Forcier from Quebec.
Justin and Karen Smith, from Los Angeles, had been hoping to go to the top of the Eiffel Tower after celebrating their wedding a day earlier in front of the monument. "We're disappointed," he said.
Police earlier told AFP that, although they had made contact with the climber, they did not know his motive for climbing up its iron beams.
Target for freeclimbers
The tower is often the target of rogue freeclimbers hoping to scale one of the world's most famous structures, often for bragging rights.
But police have also been called in several times in recent years to try to thwart suicide attempts.