The versatile Tavernier has been a big hit with Millers fans during his initial loan spell, and netted on his debut against Gillingham, whilst forward Vuckic netted the only goal in the Boxing Day win at Bradford City.
Boss Steve Evans told themillers.co.uk: "It's obvious to anyone who has seen them play they have quality, and I am delighted that they have both agreed to stay."
Both lads will stay with the club until January 31st when an option to extend the deals will be looked at.
We wish them all the best.