The sale includes all bmi Regional's fixed assets and long-term liabilities, including owned and operating lease aircraft.
bmi Regional operates a fleet of 18 Embraer regional jets on scheduled services throughout the UK and Northern Europe.
The sale is conditional upon CAA approval and it is anticipated that ownership will be transferred to SAH within two weeks.
IAG chief executive Willie Walsh said: "This deal provides a future for bmi Regional and should secure around 330 jobs".
Sector Aviation is a consortium of businessmen with considerable aviation experience including the team previously referred to as Granite Aviation, led by Ian Woodley. The business is being funded by Stephen and Peter Bond who are also investors in Loganair.