McNulty, 23, has made 43 appearances for the Blades since joining from Livingston in 2014, and could be recalled by his parent club in January.
Vuckic, 24, has played seven league games for Newcastle since signing from Slovenian side Domzale in 2009.
He scored two goals in 15 League One matches on loan at Wigan last season.
"I am excited to join a big club like Bradford. I had a few options but I always wanted to come here once I knew of their interest," McNulty said.
"With the size of the club, the manager and the fan base, it was a no-brainer."
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Bradford have signed striker Marc McNulty from Sheffield United on a season-long loan and Newcastle forward Haris Vuckic until January.