The previously unreported attacks were authorised in 2004 by Defence Secretary Donald Rumsfeld, the Times quoted senior officials as saying.
The order gave US forces permission to attack terror targets anywhere in the world without prior specific approval.
The Times said the defence department declined to comment on its claims.
The White House also made no comment.
The paper said it had spoken to more than six officials, “including current and former military and intelligence officials” as well as senior policy makers in the Bush administration.
They said that the order, signed by Mr Rumsfeld with the approval of President George W Bush, was intended to make it easier for the US military to act outside officially declared war zones at short notice.
The paper’s sources also claimed that “as many as a dozen” attacks had been called off – “often to the dismay of military commanders” – due to lack of evidence or because they were considered too dangerous or “diplomatically explosive”.