The 19-year-old made two appearances for Burnley last season.
"I want the chance to play regular EFL football and hope I can make a big impression with Accrington," Bauress told Accrington's website.
Manager John Doolan said: "We need quality players coming in to provide competitition for places and that's what Joe is - a quality player.
"He is a top midfielder - he is competitive, he can handle the ball, he is box-to-box, he likes a tackle, and he dictates play - he is an all-round player.
"He has been around the First Team set-up at Burnley and has had a good pre-season.
"It's a massive signing with Joe coming from a Premier League club. We have a very good relationship with Burnley, it's on the doorstep and they can keep an eye on him. It's a top signing for us."