Homebase has submitted plans to Scarborough Council to build a 30,000sqft superstore on the old SB Woodworking site on Stainsacre Lane.
The retail giant is hoping borough councillors will give it their backing and allow the company to take over the site which has been empty since 2002.
Part of the building was damaged by fire last November leaving the site boarded up.
Tom Marshall, of Tom Marshall Associates, who owned the site and is now working with developer Stirling Scotfield LLP, said the development would be good for the town.
"I think it is the right project for the site," he said.
"What is up there right now is an eyesore and I think the proposed landscaping on the site will greatly add to the area.
"A lot of people currently travel to Scarborough or Teesside to go to large DIY stores, as there is currently nothing like this in the town.
"It is the perfect place, it will not be near any homes and is in the business park."
The application states that the new store would generate between 55 and 60 jobs, evenly split between male and female, with 40% being full-time posts.
The store will be single storey and will also comprise a garden centre and conservatory.
The car park will hold 104 cars, including five disabled and five parent and child, as well as cycle parking.
A spokesman for Homebase said: "We are pleased to confirm that leading home enhancement retailer Homebase, working with developers Stephen Holman of Stirling Scotfield, are pursuing a planning application for a new Homebase store in Whitby.
"Homebase are delighted to have the opportunity to open a new Homebase store in Whitby."
Stephen Holman, development director for Stirling Scotfield, said they were planning to hold a public consultation to show the plans to the people of the town.
"We are working with Homebase to provide them with a site at Whitby business park, a mile and a quarter outside of Whitby," he said.
"The store will offer people the chance to do their shopping at a major DIY store and develop part of the town.
"We are currently trying to organise an exhibition to show the public the plans in detail and hope to be able to announce when and where soon."
The plan will go before Scarborough councillors next month.