Police have appealed for information following the theft in the town's Clifton Road on Friday, January 6, around 1.30am.
A number of branded goods linked to computer game HALO and contained in a red plastic bag were left outside the front door of the property next to the wheelie bin, to be collected in the morning. However, in the morning the bag and contents had gone.
It included a black hooded top with HALO written on the back and an image of a soldier on the front, a black T-Shirt with HALO written on the front, a black sports holdall with halo written on each side, two posters used for marketing of the computer game HALO, one with green soldier the other with a blue solider on it, and two model HALO figure soldiers.
A police spokesperson said: "The family acknowledge that due to where the bag had been left, a passer-by may have miss thought that the items were discarded rubbish and no longer required by the family. However, this is not the case and the family and particularly the boy would like his birthday presents returned."
If anyone can assist in returning these items, or anyone who has any information, which could assist police with their enquiries, are asked to contact Selkirk Police Station on 01750 21701.