Woolsey appeared on CNN shortly after the announcement, saying he joined the Trump campaign because he favors the Republican candidate's defense budget proposal. Trump has proposed to lift the caps on defense spending. Woolsey also advised Republican John McCain's presidential campaign.

"He seems to be very much more so than his opponent in favor of a strong defense budget and we have got a lot of space to make up, problems that have been left in defense by the Obama administration," Woolsey said on CNN Monday, adding that Trump is more willing to keep classified information private.

"He seems willing to keep a secret and not to blab everything to the public and our opponents. You can't go yakking about everything you're interested in. You have to keep your counsel," Woolsey said.