Banks Renewables is behind the project close to Birneyknowe Cottage, south east of Hawick.
Planning officials had advised opposition due to its landscape, visual and cultural impact.
The size of the project means that the final decision on whether it goes ahead lies with the Scottish government.
The company has said the project would provide a Â£2.5m community benefit fund to support local groups and good causes.
Councillors in the Borders have unanimously agreed to lodge an objection to a 15-turbine wind farm near Bonchester Bridge.