"I am very much looking forward to a new challenge and the opportunity at Edinburgh Rugby ticked all the boxes," Cockerill said in a statement.
"It's a real rugby city, and the club has a lot of potential to grow on, and off, the pitch."
Edinburgh's acting head coach Duncan Hodge will stay in charge until the end of the season before returning to his previous position of backs coach when Cockerill takes over.
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Edinburgh's assistant coaches Stevie Scott and Pete Wilkins remain in their posts.
(Reporting by Simon Jennings in Bengaluru)
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