"Heather Wilson is going to make an outstanding secretary of the Air Force," Trump said in an announcement.
"Her distinguished military service, high level of knowledge, and success in so many different fields gives me great confidence that she will lead our nation's Air Force with the greatest competence and integrity. Our debt to America's men and women in uniform is eternal. Their service is an inspiration to us all, and we honor their service and sacrifice," Trump said.
Wilson would be the third woman to serve in the role after Deborah Lee James, who served under President Barack Obama, and Sheila E. Widnall, who served under President Bill Clinton's administration.
"America and our vital national interests continue to be threatened," Wilson said in the statement. "I will do my best, working with our men and women in the military, to strengthen American air and space power to keep the country safe."
Republican Rep. Mac Thornberry of Texas, chairman of the House Armed Services Committee, said, "Heather Wilson is an excellent choice for secretary of the Air Force. Having served with her on the House Armed Services and Intelligence Committees and worked with her on many issues, I know her to be a serious and thoughtful leader who is well-equipped to meet the challenges we face in national security. I look forward to working with her in this new role."
Wilson graduated from the U.S. Air Force Academy in 1982, part of the third class to include women, according to the White House statement.
She earned both master's and doctoral degrees as a Rhodes Scholar at Oxford University in England, while in the Air Force.
She served as an officer in Europe and, after leaving the service in 1989, served on the National Security Council staff at the White House under President George H.W. Bush during the fall of the Berlin Wall, according to her biography.
Wilson served as a Republican in Congress from 1998 to 2009, representing New Mexico's 1st Congressional District. She chaired the House Subcommittee on Technical and Tactical Intelligence, and was a senior ranking member of the the House Energy and Commerce Committee. She also served on the House Armed Services Committee for four years.
She ran in 2008 for a Senate seat, but lost during the primary election.
Since 2013, Wilson has been president of the South Dakota School of Mines & Technology in Rapid City. The public institute focuses on degree programs in engineering and science fields.
Wilson, from Keene, New Hampshire, is married to Jay Hone, an attorney and retired Air Force colonel, the White House announcement said.
Until Wilson is confirmed, Air Force Undersecretary Lisa Disbrow will serve as the service's acting secretary, the Air Force said Monday.
Editor's Note: This story has been updated with information on the service's acting secretary.