Barrett, 68, a wealthy Republican donor and wife of former Intel chief executive Craig Barrett, has served as the Chairman of the Aerospace Corp -- a non-profit corporation based in California that operates a federally funded research and development centre for the space enterprise, the Washington Post reported.
Trump made the announcement on Tuesday on Twitter, saying: "She will be an outstanding Secretary!"
Barrett was the US Ambassador to Finland from 2008 to 2009 under the George W. Bush administration. She also served on the board of the National Air and Space Museum, the Rand Corporation, Sally Ride Science and the Space Foundation.
If confirmed, she will be the third woman in a row to serve in the top civilian position at the Air Force.
Barrett would also join acting Defence Secretary Patrick Shanahan in an attempt to win congressional support for plans to establish a separate Space Force under the Air Force, one of Trump's top priorities for the service.
Wilson submitted her resignation in March.
Barrett is also a certified astronaut, having spent time at the Gagarin Cosmonaut Training Centre in Russia and the Baikonur Cosmodrome in Kazakhstan to become the backup crew member for Cirque du Soleil co-founder Guy Laliberte when he travelled to the International Space Station as a space tourist.
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