Donald Trump's transition into office will be unique because he has few strings attached when it comes to government, George H.W. Bush transition co-chair Craig Fuller told CNBC on Monday.

Fuller said Trump should have a certain freedom in picking his Cabinet and working with Democrats because he is not a partisan Republican and lacks a voting record.

"I haven't seen a president-elect that really has more freedom," Fuller said on "Squawk Box."

Trump's transition team announced Sunday that it would name Reince Priebus, the chairman of the Republican National Committee, as the president-elect's chief of staff.

The team also named Breitbart News' Steve Bannon as Trump's chief strategist. Bannon was CEO of Trump's presidential campaign.

Fuller said one of the most important things for Trump to focus on are the top 100 jobs he fills during transition.

"There has to be a balance. Really, there need to be people who are new, fresh, bringing new ideas, but you also have to have people who understand how the mechanisms of Washington work," Fuller said.

And while Fuller acknowledged that the transition is a daunting task, he was pleased with Trump's choices so far.

"I think Reince Priebus is a good choice because he does know Washington, he does know the players here, but he's also … been out all over the country so he understands the pulse of the country as well," Fuller said.

As for Bannon, Fuller said his role would be to help push Trump's political agenda through Congress by addressing the way the president communicates and shapes public opinion.

"There's … an old saying in Washington that sometimes 'to see the light you have to feel a little heat,'" and Bannon would surely bring the heat to a Trump administration, Fuller said.