Dawson became the third player to swap White Hart Lane for the KC Stadium this week when he joined in a £3.5 million deal.
That trio - Dawson, Huddlestone and Jake Livermore - have all been capped by England and cost the Tigers a combined £15m.
Huddlestone said: "I was surprised Spurs let him go to be honest, because even last season he played near enough every game for them. It was a bit of a surprise because he's only 30 so hopefully we can get three or four good years from him.
"Spurs' loss is our gain. They've obviously got a new manager [Mauricio Pochettino] who is trying to do things his own way and wants his own players which is fair enough, but hopefully we can benefit from that with the signing of Daws."
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