The experienced Republic of Ireland international arrives on a four year contract after his contract at Burnley expired.
Hendrick played 24 Premier League games last term.
On his arrival, Bruce said: "Jeff is someone I've admired for a long time. I watched him when he was at Derby, then he went to Burnley for a lot of money and couldn't afford him, so I missed out then!
"He's an experienced international football who can play all across the midfield so we welcome him aboard. He'll be a big asset to us, on and off the pitch.
"He's a great pro, down to earth, and at the age of 28 it's a wonderful time to get somebody. It is the peak of his career - he's a really fit boy who has played 122 times in the Premier League for Burnley over the last four years, and I'm sure he'll be a great addition to the squad."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!