The 24-year-old has joined Leonid Slutsky's side for an undisclosed fee, signing a three-year deal, with the option for a further year.
Ivrine was a key man for the Brewers as they successfully avoided relegation from the Championship last season, scoring 10 goals in 42 Championship appearances.
The Australian scored against his new employers earlier this season, albeit in a 4-1 defeat.
Upon completing the move, Irvine told Hull's official website: "I couldn't be happier and I'm just excited to be starting the next chapter of my career,"
"It has all happened relatively quickly, but once I found out about the interest from Hull City it was an easy decision even though leaving Burton was difficult in its own way.
"I just can't wait to get started now."
| Welcome, @jirvine36!
— Hull City (@HullCity) 30 August 2017
We are delighted to confirm the signing of Jackson Irvine from @burtonalbionfc #WelcomeJackson pic.twitter.com/3L6ioFdzDq