If his nomination is confirmed, he will replace Suzi Levine, who resigned after Trump's election victory last November.
McMullen Jr is a New York native who has lived in South Carolina for more than 30 years, where he is a public affairs consultant. He was Trump's campaign chairman in the state during the primaries before becoming a member of the president-elect's transition team.
His appointment fills a vacancy left open by Levine, who left her post on January 20th, the day of Trump's inauguration.
The nominations still need to be approved by the US Senate, where Trump's Republicans hold a majority.
McMullen Jr's nomination comes as part of a slew of ambassador appointments to key capitals, including Berlin and New Dehli, announced by the White House on Saturday.
Media commentator Richard Grenell is nominated as ambassador to Germany. If confirmed, the prominent Trump supporter would be the first openly gay appointee of Trump's administration, US media reported.
The president has been criticized for his slow pace in filling ambassadorial and management posts at the State Department.
Secretary of State Rex Tillerson, the former ExxonMobil chief, has a plan to slash by 30 percent the budget of an agency that employs more than 70,000 people in Washington and around the world.