Saved selections are merely alpha channels in Photoshop.
You can copy channels between files by simply dragging the alpha channel from the Channels Panel of the old document to the window of the new document. This will create a new alpha channel in the new document. The selections will then appear in
Select > Load Selection.... If your documents are the same dimensions, the alpha channels will be in the same position in both documents. Holding down the Shift when dragging ensures the dragged channel is placed in the same relative position as the old channel if the two documents are different dimensions.
Another method is to simply Right-Click/Control-Click the alpha channel and choose
Duplicate Channel... from the contextual menu. When the duplicate options dialog pops up, select the document you want to duplicate the channel to and hit OK.