FIFA run a Transfer Management System for international transfers.
http://www.dailymail.co.uk/sport/football/article-3212646/FIFA-s-Mark-Goddard-explains-handle-deadline-day-rush-using-International-Transfer-Management-System.html
This system was introduced in 2010.
Before that, FIFA were...
From the club twitter feed:
BHAFC @OfficialBHAFC 30 Dec 2015
Both players require international via FIFA and international transfer window does not reopen until 4th Jan to apply. (2 of 2) #BHAFC