The FTSE 250 firm said Browett, former boss at Dixons and fashion chain Monsoon Accessorize, was standing down “for personal reasons”.
But despite the “good progress” under his leadership, including the acquisition of online retailer Worldstores, it claimed the next phase of growth “requires different leadership”.
Chairman Andy Harrison will take on the role in the interim.
He said: “I would like to thank John for his contribution to the business and the strategic progress made under his leadership, most notably the exciting acquisition of Worldstores.”
Mr Browett said in a statement: “I am pleased to have led the development of Dunelm over the last few years and feel that we have achieved much in a challenging retail environment.
“It is, however, time to move onto a new challenge, and I am looking forward to the next chapter of my career.”
Nick Bubb, an independent retail analyst, said: “Dunelm was always an odd choice after his time at Dixons and Apple, and he never seems to stay in jobs for that long.”
Shares fell 24½p to 573½p.