"Jim Mattis is someone I've known extremely well," Mullen said. "He's an incredibly capable individual, strategically focused internationally focused. He has good relationships on the international side and I think someone who is born to serve and could make a difference, really significant difference as well."
As chairman of the Joint Chiefs of Staff under Presidents George W. Bush and Obama, Mullen held the nation's highest-ranking military office and served as the principal military adviser to each president.
He said the new president will face significant challenges "on day one," including North Korea's nuclear ambitions and ISIS. “The world is very unforgiving,” he said.
Mullen has written that the next commander-in-chief will likely face a North Korea that has gained a capability to use a nuclear weapon against the U.S.
“I think ... that peninsula is more likely than anybody place else in the world to potentially create an explosive outcome, particularly tied to the North Korean leader Kim Jong Un," Mullen said.
"Four of the five top economies in the world are centered" in that region, he added. "Stability there is critical."
Mullen acknowledged that the policies of Bush and Obama were unable to stop the advancement of North Korea's nuclear program and said China will have to play a key role to keep the region safe.
“I think actually this has to go through Beijing -- and Beijing has pushed back on that time after time,” he said.
“But if Beijing doesn't leave this, we're going to get to the point where [Jong Un] is going to be able to put a nuclear weapon on top of an intercontinental ballistic missile that could hit the United States, and that's unacceptable," Mullen said.
When asked about Trump's claim during the campaign that he knew more about ISIS than “even the generals,” Mullen said, "I would put that in a category of rhetoric on one side and reality on the other."