"It appeared he might be trying to go over the fence so the uniformed officers grabbed him," the Secret Service spokesman, Karl Meyer, said. Bello was not armed.
At the time, the Clintons were in the White House celebrating Christmas after attending a church service. "At no point were they ever in any danger or for that matter did they even realise what was going on," Mr Meyer said.
Bello was charged with unlawful entry and making threats after arguing with police during his arrest.
Mr Meyer said arrests of fence climbers "happen regularly" at the White House. He called the Christmas morning incident a "routine occurrence."
There have been fears, however, that a series of recent assaults on White House security might bring a rash of copy-cat incidents. A small plane crashed on the South Lawn in September, killing the pilot.
This was followed in October by the arrest of Francisco Martin Duran, who opened fire on the front of the building with a semi-automatic rifle.
He was charged with 15 felony counts, including attempted assassination of the president.
In the last two weeks, four shots were fired at the rear of the White House in what police said could have been a random drive-by shooting.
Police shot and killed a homeless man who brandished a knife on a pavement in Pennsylvania Avenue; a man was arrested after claiming there was a bomb in a car outside.
Another was arrested and charged with carrying an unregistered firearm after being seen standing near the fence at 2am, and a man was taken into custody after he slipped into the White House grounds through an open gate.