Reince Priebus, chairman of the Republican National Committee (RNC), will be his chief of staff.
Stephen Bannon, from the right-wing Breitbart News Network, will serve as Mr Trump's chief strategist.
Bannon was Trump's campaign chief.
"Steve and Reince are highly qualified leaders who worked well together on our campaign and led us to a historic victory. Now I will have them both with me in the White House as we work to make America great again," Trump said.