© UnknownTotnes currently has 41 independent coffee outlets
South Hams District Council had approved plans by Costa Coffee to open in Fore Street, Totnes.
But in a letter, Chris Rogers, managing director of Costa, said the company had "recognised the strength of feeling" against national brands in the town.
The move, detailed in a letter to "the people of Totnes", has been welcomed by campaign group No to Costa.
'Sensible decision'
The town boasts 41 independent coffee outlets and is well-known in the South West for its "alternative" image, with a resident community of artists, writers, therapists, musicians, and herbalists.
In the letter, Mr Rogers said the decision had been made following a discussion with different groups in the town.
"Costa has recognised the strength of feeling in Totnes against national brands and taken into account the specific circumstances of Totnes," it said.
Public relations analyst Phil Morgan said the decision to pull out of Totnes could benefit Costa in the long-run.
Mr Morgan, of the Chartered Institute of Public Relations, said: "The option would have been to open the branch and face hostility - for an initial period at least - as well as possibly gaining a reputation for ignoring the wishes of people in the towns and cities where they set up shop.
"On the face of it, this is a sensible decision for a growing business. Responsiveness is key to building trust and reputation, and as important as the quality of their coffee."
© UnknownCosta has more than 1,390 shops across the UK
Costa's letter was also signed by Dr Sarah Wollaston, MP for Totnes, and Pruw Boswell, Mayor of Totnes.
In the letter, Dr Wollaston and Ms Boswell said: "As your MP and Mayor, and speaking on behalf of the people of Totnes, we would like to thank Costa for being prepared to listen to our concerns and showing that they care."
Previously, Ms Boswell said: "It's so alien to what the town's about."
No To Costa spent three months petitioning against the planned coffee shop, which was due to take one of the larger retail spaces in the town. It collected more than 5,000 signatures.
Tony Kershaw, from the organisation, said: "We're happy with the decision Costa has made.
"Totnes, as most people know, is pretty independent and different as a town, and we're seeking to protect that."
Various businesses in the town have said they are "delighted" at the news.
Retail guru Mary Portas also congratulated the company on its decision.
On Twitter, she said: "Applaud CostaCoffee for listening to Totnes before opening. Shame South Hams Council didn't b4 granting permission."
But taxi driver Steve Davey said he and other many other drivers were disappointed.
'Reality check'
"We are coffee experts," he said.
"There may be 41 coffee shops in Totnes, but there are only a few that are any good.
"We have got Morrisons and a lot of other big retailers in the town.
"I can't see the problem with having a Costa Coffee."
Tim Jones, of the Devon and Cornwall Business Council, said the campaign had sent out the wrong signals for the town.
"They need to have a reality check on what this is telling the market place," he said.
"If Totnes is going to grow and thrive it needs to embrace commercial development.
"It can't throw these barriers up and isolate itself from the realities of the market place, however well-meaning that might be."
But Holly Tiffin, from eco-group Transition Town Totnes, said: "It perhaps sends out a clear message to other chains that this isn't the place to come but it really opens it up for entrepreneurs and local businesses by saying that here you can really set root and flourish."
Costa currently has 19 stores in Devon and employs nearly 200 people as well as sourcing local products.
It has more than 1,390 shops across the UK, employing more than 10,000 staff, and another 800 internationally.
Earlier this month, the coffee shop chain, which is owned by the Whitbread group, reported its 42nd consecutive quarter of growth, with profits of £36.1m.
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