Businessman John Wilson has also been given the thumbs up to build a detached house in the garden ground at Bogsbank Road in West Linton.
The application had attracted opposition from most neighbours as well as local councillors.
Tweeddale West member Catriona Bhatia argued that the plans contravened planning policies.
She told Monday’s planning meeting: “The building line is pretty clear along Bogsbank Road. This is a backland type development and doesn’t accord to our policies. The neighbouring properties are linear and this breaks with the line.”
The councillor also argued that the new-build would be to the detriment of the conservation area.
She added: “There is an opportunity for a house to be built on this site - but in line with other houses and I would urge the developer to come back with a revised proposal.”
A total of 17 objections to the plans for the former police station were lodged with Scottish Borders Council. Caroline McDonald, who lives in the neighbouring property, told Monday’s planning committee: “The current application has shocked many of us. The proposed new house sits well back from the current housing line.”
But the arguments against the plans didn’t win much support in the chamber.
Members were also told that amendments had been made to the plans to appease some of the concerns raised by neighbours.
A motion to reject the application, made by Councillor Donald Moffat, only gained support from his colleague, Bill White.
And seven members agreed with their officers to pass the plans.
Tweeddale East member Stuart Bell said: “I don’t find it an unacceptable application regarding the conservation area, and I’m not convinced by the building line argument.”