Kevin Brown, who is also the current managing director of Southampton Airport, will replace Gordon Dewar.
Stephen Peat, managing director of BAA, airports division, said:
"Whilst Gordon leaves Edinburgh Airport in a strong position, Kevin takes the reins at a time of huge challenges for our industry.
"I am confident that he will lead this vital part of Scotland's economy into its next stage of development and success."
Mr Brown has also held positions at Heathrow.