12,190 (76%) electors voted against having a directly elected mayor and 3,555 (22%) voted in favour of the option. There were 351 spoilt papers. A total of 16,096 ballot papers were returned.
The outcome of the poll now means that West Devon BC will adopt a streamlined committee system as its decision -making structure.
David Incoll, chief executive of West Devon BC and referendum counting officer, said: ' What is the most pleasing about this exercise is the response of local people.
'Their willingness to vote shows that they care about how their council operates.'
West Devon's ceremonial mayor Robin Pike said: 'The result today was achieved by the true democratic process and the people of West Devon exercised their freedom of choice.
'I would like to thank everyone who took the time to vote and decided for themselves the way they wish to be governed locally in the 21st century.'
The Electoral Reform Service carried out the postal ballot and the votes were counted at the service's London headquarters.
The referendum was called as part of the Local Government Act 2000 where parliament requires councils across the country to choose one of four options in the way they manage their business.
Two polls carried out in West Devon last year showed that there was a significant interest for change in the borough. And a majority of West Devon councillors felt a referendum was the best way forward so that the public could have its say on the future of the authority.
Nationally, West Devon is the 21st authority to hold a referendum on the mayoral issue. To date, not including West Devon, seven authorities have voted for a directly-elected mayor whilst 13 have voted against.