Mr Bridenstine, 42, who backed President Trump during the US presidential campaign, had long been considered the favorite for the job of NASA administrator.
But the nomination drew fire from two US senators from Florida who questioned the Oklahoma representative's qualifications to lead such a complex and highly technical agency.
Senator Bill Nelson, the ranking Democrat on the committee that oversees NASA, told the news site Politico the agency's new leader should be "a space professional, not a politician."
Mr Marco Rubio, the state's other senator and a Republican, said the choice of Mr Bridenstine "could be devastating for the space program."
"I would hate to see an administrator held up- on [grounds of] partisanship, political arguments, past votes, or statements made in the past- because the agency can't afford it and it can't afford the controversy," he told Politico.
Mr Bridenstine, who was elected to Congress from Oklahoma in 2012, is a member of the House Armed Services Committee and the Committee on Science, Space and Technology.
According to the trade publication SpaceNews, Mr Bridenstine has been a big proponent of giving the private sector a larger role in space.
The space agency is involved in all aspects of space exploration, as well as in Earth observation missions from space and in the development of new aerospace concepts.
NASA is currently developing a heavy launcher and capsule capable of taking astronauts to Mars in 2030 and beyond.
But it faces competition from billionaires like Amazon CEO Jeff Bezos and Elon Musk, who runs SpaceX and Tesla.
NASA's proposed 2018 budget comes to a little more than $19 billion.
Mr Bridenstine's experience is mainly in the military, as a pilot who flew combat missions in Iraq and Afghanistan, and as a member of the naval reserves has flown counter-drug missions in Central and South America.
He served as executive director of the Tulsa Air and Space Museum and Planetarium. He is also a member of the Oklahoma Air National Guard.
He has degrees from Rice University and Cornell.