He will be replaced by Phil Wrigley, who was, until recently, chairman of the clothing retailer New Look – and before that was its chief executive.
He has also held senior management positions with Debenhams, Arcadia and BHS.
He is currently chairman of LXB Retail Properties.
Chief executive Steve Lewis said: “His broad retail and property experience will be invaluable in continuing to grow the Majestic story.”
Wrigley will join the Majestic board in April and take over the chair when Burke leaves at the next AGM.
Burke joined the Majestic board as non-executive director in 2000 and has been chairman since 2005.