The 21-year-old Slovenia forward follows right-back James Tavernier to the New York and will stay in South Yorkshire until early 2014.
Boss Steve Evans said: "This is a fantastic signing and he is a player we look forward to working with.
"He certainly adds a lot of quality to a very talented squad.
"We have signed three new players in a week; Nouha Dicko, James Tavernier and now Haris.
"I am again grateful to Alan Pardew and Newcastle United Football Club. The lad will train with us and all being well will also be in contention to make his debut on Saturday."
If the deal is ratified by the Football League, Vuckic, who spent time on loan at Cardiff last season, could be involved against Gillingham on Saturday.