Supporters will get their first glimpse of the 26-year-old in City colours when he features against either North Ferriby United or Harrogate Town on Monday night.
Bruce told the Hull Daily Mail: "Snodgrass ripped us to bits down at Norwich last year.
"I've always seen him because he played with my son (Alex) at Leeds and I always liked him.
"There's a natural ability to beat a player and he's got great deliveries. He's 26 and in his prime. We were short in wide areas last year and he'll give us a supply line.
"Not just that, he offers you goals. Everyone in the Premier League is disciplined and has good players so the hardest thing is scoring goals. He can add another string to our bow."
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