Police have charged a man with murder over the death of Greenslopes mother Danielle Miller.

The 49-year-old Annerley man, Robert Graham Thomas, was arrested on Wednesday morning while buying fish and chips at a Coorparoo takeaway shop, police say.

Robert Graham Thomas is led out of Dutton Park Police Station by police. Credit:Nine News

He faces one count of murder and six counts of stealing.

Mr Thomas, who was questioned by detectives at the Dutton Park Police Station, was taken to the Brisbane Watchhouse where the charges were laid.