The Range, the home, leisure and garden retail chain, is preparing to move to the former B&Q site at Liverton Business Park.
As part of its plans, it is proposing the garden centre building, to be used with the existing main building, which will stock plants, garden equipment, and garden furniture.
Exmouth Town Council’s planning committee will be consulted on the application, before East Devon District Council decides on permission.
The Range previously announced its new store, to open later this year, would create 80 jobs, in a mix of full-time and part-time roles.
The previous B&Q store had been trading at the site for more than 20 years before its closure in November last year.