"I think the president-elect is going to select the people that he thinks will do the best job. That's what I've been most impressed about following the election, acknowledging the gravity of the job in front of him and the challenges our country faces and he wants to get the best people in there," Miller said on the ABC News' "Powerhouse Politics" podcast.
"I think that's something people have a lot of respect for...when he said 'Hey, these guys may have been political rivals, maybe we've butted heads before, but you know what, now we're on the same team and we got to go and lead the country,'" Miller added.
Cruz and Trump had numerous public battles, with Trump repeatedly calling him "Lyin' Ted." "This man is a pathological liar," Cruz said of Trump in May. "He doesn't know the difference between truth and lies. He lies practically every word that comes out of his mouth."
Trump also took his shot at Cruz during an interview with ABC News' "This Week." "As far as Ted Cruz, he's one of the greatest liars and biggest liars I've ever known. He lies about so much," he said. "He lies about things that he shouldn't be lying about. He lies about things that don't matter.”
"His foreign policies would make America and the world less safe. He has neither the temperament nor the judgment to be president and his personal qualities would mean that America would cease to be a shining city on a hill," he said in March.
Later that month, Trump said: "I don't think Mitt Romney is a smart person. I never have thought he was a smart person." He also questioned Romney's faith.
Miller called Trump's upcoming meeting with Romney "a great opportunity."
"I think it's a great opportunity to learn from someone who's been very successful in business himself and who's seen the world stage," Miller said. "Governor Romney definitely has some good ideas to share."
Although Trump has only appointed Reince Preibus as chief of staff and Steve Bannon as chief strategist, Miller said other announcements could come "pretty quickly."
"I think the president-elect is very close to knowing who he wants to go with," he said, "When the president-elect feels he got it right he will be the one making the decision and we will take it from there."
When asked if Trump would enter office with a fully formed cabinet, Miller responded, "I think he's gonna get it right."
Miller also addressed reports that the Trump children, who are expected to take over the family businesses from their father when he is sworn in, will have official roles in the White House, calling them "overblown."
"They are a support structure," Miller explained. "Obviously they're gonna be available if he calls."