Brady, a 23-year-old winger, made 43 top-flight appearances for Hull, who are now in the Championship (second tier), during the last two seasons and has won 14 international caps.
"He'll be an absolutely perfect fit for us," Norwich manager Alex Neil told the club website (www.canaries.co.uk).
"He's dynamic, he's got good energy to get up and down the pitch and he's got a fantastic left foot which makes him a real danger at set pieces. He's got a lot of things in his locker."
Former England under-21 defender Wisdom joins on a season-long loan deal from Liverpool where he recently signed a new long-term contract.
The versatile 22-year-old, who can play at centre back or at right back, spent last season on loan at West Bromwich Albion where he made 24 appearances.
"I’m delighted as Andre fits our profile in terms of getting hungry players in who want to make their way in the game," Neil said.
Brady and Wisdom are Neil's third and fourth signings since Norwich gained promotion and follow the arrivals of Scotland midfielder Graham Dorrans, 28, from West Brom, for a reported fee of three million pounds ($4.70 million) and DR Congo midfielder Youssouf Mulumbu, 28, on a free transfer.
(Reporting by Timothy Collings and Toby Davis, editing by Alan Baldwin and Ken Ferris)
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