Tavernier and Vuckic both joined in November and have played an important role as the Millers have consolidated a position in the League One play-off positions.
Boss Steve Evans told the club's official website: "It's fair to say that both lads have helped raise the standard in training and in games, and I believe there's still much more to come from both of them.
"James has really hit the ground running and he's been a key component in the recent good results we've had, and Haris is very quickly acclimatising to a level where it's about finding space to allow him to unleash the outstanding natural talent that he possesses which makes him a Premier League player."
Tavernier has had more of an impact during his time at New York, making 11 appearances, while Vuckic has had a more sparing role, making five starts.
Source PA