Kee scored 12 goals in 14 starts for Albion last season but missed most of the second half of the campaign due to a groin injury.
The Northern Ireland Under-21 international, who joined Burton 12 months ago from Torquay, is now back in action and scored in the recent 6-2 home win over AFC Wimbledon.
"I've really enjoyed my time here so far so I'm delighted to have signed a new contract," Kee told the club's official website. "I've settled here - we're like a big, happy family - and you can see that with the way my football has come on in the last year. I did well last season and now the club have rewarded me for getting back fit."
Albion boss Gary Rowett added: "Billy was coming into his last year and, after his goal exploits last year and his age and international prospects, I felt as if he was somebody we definitely wanted to tie down for the longer term.
"I'm really pleased that, after three of four weeks of talking to him, it's come to fruition. Billy has worked really hard over the summer. He's shown a real commitment to the cause. He's expressed his enjoyment to be at this club and, if he's enjoying his football and his environment, he'll score goals."
