"I think it would be disastrous. It really would," Mr. Brennan said in a BBC interview.
"First of all for one administration to tear up an agreement that a previous administration made would be unprecedented."
He said such a move would risk strengthening hardliners in Iran and risk other states pursuing nuclear programs in response to a renewed Iranian effort. "I think it would be the height of folly if the next administration were to tear up that agreement," he said.
Brennan also advised the new president to be wary of Russia's promises, blaming Moscow for much of the suffering in Syria.
"I think President Trump and the new administration need to be wary of Russian promises," Mr. Brennan told the BBC, arguing Moscow had failed to deliver in the past.
Read alsoTrump names pro-Ukraine CIA DirectorOn the role of Russia in trying to influence the U.S. election by hacking and releasing information, the CIA director confirmed Russia had sought to carry out such activity but said he would defer to domestic counterparts as to the impact.
He did confirm that he had conversations with his Russian opposite numbers to challenge them over these actions and warn them that such activity would backfire.
The U.S. should not "stoop to their level" or risk escalation by responding in kind to Russian hacking, but he said there were other ways of ensuring Russia understood such activity was unacceptable.
As UNIAN reported earlier, U.S. President-elect Donald Trump moved to fill some of the top positions in his government by selecting a Central Intelligence Agency (CIA) director, a national security adviser, and an attorney general.
Read alsoBritain expects Donald Trump to 'stand up' to RussiaTrump said he had chosen Representative Mike Pompeo (Republican-Kansas) to be CIA director, retired General Michael Flynn for the post of national security adviser, and Senator Jeff Sessions (Republican-Alabama) as the country's top prosecutor.
Pompeo, who is currently a member of the House Intelligence Committee is known in particular for his statements in support of Ukraine in its resistance to Russian aggression.
In April 2014, Mike Pompeo visited Ukraine and then stated that the aim of Russian President Vladimir Putin was to take control over Ukraine.
Read alsoPoroshenko says Trump asked to elaborate on Russian aggressionHe stressed: "To the degree that we can demonstrate support for the Ukrainian government, we can change Putin's calculus and increase the risk to him and to Russia for moving combat forces closer to Kyiv."
Pompeo and Sessions require confirmation by a majority vote in the Senate; Flynn does not.
Pompeo is a member of the Republican Party's conservative wing, the Tea Party, having been elected to the U.S. House of Representatives in 2010.
He graduated top of his class from the U.S. Military Academy at West Point and graduated from Harvard Law School before spending five years in the army.