The Australian international midfielder joins the Tigers for an undisclosed fee following just over a year with Burton, where he scored 11 goals in 49 appearances - including one against Hull earlier this month.
The 24-year-old has put pen to paper on a contract which will keep him at the KCOM Stadium until 2020, with the option of a further year on top of that.
"I couldn't be happier and I'm just excited to be starting the next chapter of my career," Irvine told the club's official website.
"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."
Irvine could make his Hull debut when they take on Derby County after the international break.