Irvine, who first arrived in Britain from Australia in 2010 when he joined Celtic's youth team, has agreed a three-year contract at the KCOM Stadium.
"I couldn't be happier and I'm just excited to be starting the next chapter of my career," Irvine told his new 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.
Irvine is currently part of the Australia squad for upcoming World Cup qualifiers against Japan and Thailand and is in line to make his Tigers debut against Sunderland when domestic football resumes early next month.
Irvine has actually played and scored against Hull already this season.