Steve Lewis, who has been chief operating officer at the wine warehouse chain for the past two years, will take over from How when he retires later this year.
How, 57, has been credited with leading Majestic from a small loss-making chain to a successful, profit-making wine retailer with 141 stores.
Majestic chairman Simon Burke, said: "Along the way he has created tremendous value for shareholders, acquired a loyal and dedicated customer following, and built a highly professional retail and management team. He has been a truly great chief executive and we all owe him a huge debt of gratitude. We wish him a long, happy and prosperous retirement."
How will stay on with the company for a handover period with Lewis, who has worked his way up through the Majestic ranks after joining as a graduate trainee manager in 1985.