Quoting US and Libyan rebel officials, the newspaper said the shipments were mostly of small arms such as assault rifles and ammunition.
It appeared to be the first case of an outside government arming the rebel fighters.
Rebels have been losing ground for days in the face of an advance by forces loyal to Muammar Gaddafi.
The rebels have, however, been buoyed by the United Nations Security Council's authorisation of air strikes to curb Col Gaddafi's forces.
Egyptian weapons transfers began "a few days ago" and are continuing, a senior US official told the newspaper.
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