He will succeed Edward Pysden, of law firm Eversheds, at the Halle Concerts Society's annual meeting later this month.
Mr McKeith was until recently a director of Manchester's Royal Exchange Theatre.
Today he said: "My wife and I have been fans of the orchestra for many years, so it is a great privilege to be appointed in this role. Edward has done a fantastic job over the last 10 years and will be a very hard act to follow.
"I'm joining at an exciting time in the Hallé's history and look forward to working with music director Sir Mark Elder, the board and all the staff."
Executive search firm Odgers, Ray and Berndtson was involved in the hunt for a new chairman.
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