McKie, who spent six years at the SRU before being appointed chief executive of the Hong Kong Football Association, takes the role with immediate effect.
"I have known Gordon for several years and I believe he is the man to chair the club at this stage," Sale owner Brian Kennedy said.
"He is highly respected within the game of rugby union and his commercial, organisation and administration experience will be of great benefit to the club."
McKie added: "I am pleased to take on this new challenge at this stage in my career and become involved again with sport.
"In my capacity as chairman, I look forward to working with the board and supporting the management team, the staff and the loyal supporters in contributing to the future success of the club."