"There's a fine line between stubbornness and the positive side of that, which is dogged determination," the Republican former governor said on "CBS This Morning."
"And I think what people will begin to see is that he wasn't stubborn," he said. "He was totally determined and principled about it. And the country was safer because of it. That will be the positive legacy of George W. Bush."
Jeb Bush said stubbornness doesn't run in the family, but "maybe in the case of my brother."
He said he admired the former president's physical and mental discipline.
"To take the beating he took and to stay on course, I admire it tremendously. I'm not sure I would have -- I probably would have lost my temper. I think a lot of people would have lost their temper actually."
Of his father, former President George H.W. Bush, the former governor said: "He's my total hero. I mean, I've never met a man as near perfect as George H.W. Bush."
He said his father treated everyone with decency and respect.
The two ex-presidents have a "very close relationship" and are in "continual contact," he said.