Story highlights James Woolsey is a former CIA director under Republican and Democratic administrations

He told CNN Monday that after meeting with Trump last week, he'll advise his campaign

(CNN) A former CIA director under President Bill Clinton joined Donald Trump's presidential campaign Monday as a senior adviser, the campaign announced.

James Woolsey, a former national security official under Republican and Democratic administrations who has been a fierce critic of President Barack Obama, said in a statement he will advise Trump "on the urgent need to reinvest in and modernize our military in order to confront the challenges of the 21st century."

"Mr. Trump's commitment to reversing the harmful defense budget cuts signed into law by the current administration, while acknowledging the need for debt reduction, is an essential step toward reinstating the United States' primacy in the conventional and digital battlespace," Woolsey said in a campaign statement. "Mr. Trump understands the magnitude of the threats we face and is holding his cards close to the vest."

Woolsey told CNN's "At This Hour" that he met with Trump on Friday and has agreed to advise the campaign "principally if not exclusively on national security matters such as defense, intelligence, maybe some aspects of energy ... whatever he needs."

One reason Woolsey said he supports Trump is that the Republican presidential nominee "seems willing to keep a secret and not to blab everything to the public and our opponents."

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