A report said that if the Locharbriggs facility was shut it would save at least an estimated Â£10,000-a-year.
All the staff and police officers will be transferred to Loreburn Street in Dumfries, about three miles away.
A Dumfries and Galloway Constabulary spokesman said there had been no adverse comments during the consultation process.
Concerns were voiced last month after a memo revealed plans to shut the station at the end of March.
It was blamed on a managerial error and Chief Constable Pat Shearer insisted no decision had been taken on its future.
However, police have now been given approval to close the site with a "commitment to maintaining existing levels of service" to the community.
Councillors have agreed to close a Dumfries and Galloway police station as "surplus to requirements".