Irvine, a 24-year-old Australian international, has put pen to paper on a three-year deal which also includes the option of an additional year.
Born in Melbourne, Irvine moved to the UK to join Celtic’s youth set-up in 2010 and played for Ross County before joining Burton just over 12 months ago.
Since then, he has scored 11 times in 49 appearances for the Brewers, including a fine strike against the Tigers at the KCOM Stadium earlier this month.
Irvine is delighted to become the latest addition to Leonid Slutsky’s squad in East Yorkshire, saying: “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.”
You can watch Jackson in action on home soil for the first time when Sunderland visit the KCOM Stadium next month. Tickets are available to buy here.