The girl was reported missing in Galashiels on Sunday evening, prompting a large-scale search operation involving a police helicopter, mountain rescue teams, and specialist divers.
Members of the public also joined the emergency services in the search, which went on until Monday evening, with support also provided from the Scottish Fire and Rescue Service.
Police Scotland chief superintendent Catriona Paton described the scale of the search as “a huge operation”, and praised the response from the community as “really encouraging”.
The child was last seen in Galashiels town centre around 5:45pm on Sunday and she was reported missing later that night.
In a statement issued on Tuesday afternoon, the force said the girl had been traced at a property in the Galashiels area the following evening.
The force said: “A 53-year-old man has been arrested in connection with the disappearance of an 11-year-old girl from Galashiels, who was reported missing on Sunday, February 5.
"The girl was traced at a property in the Galashiels area around 9:30pm on Monday. Inquiries into the circumstances are ongoing."