The 20-year-old has put pen to paper on a four-year contract at Turf Moor until the summer of 2027 and joins the Clarets for an undisclosed fee, believed to be worth in the region of £19m.
Trafford becomes Vincent Kompany's sixth signing of the summer transfer window after the arrivals of Lawrence Vigouroux, Michael Obafemi, Dara O'Shea, Jordan Beyer and Zeki Amdouni, the latter of whom officially joined Burnley on Wednesday.
Speaking to Burnley's official website on his arrival at the club, Trafford said: "I feel very happy to officially be a Burnley player, I was excited for it to all get done whilst the Euros was going on, I knew a lot about it and I was waiting to get back to make it all official really.
"I want to improve and learn as much as I can here and as a team, I just want to take it a day at a time and try and achieve as much as we can going forward."
Kompany added: "We've signed an extremely talented young man. More than just a talent he's a great character.
"James is a very impressive, confident mature young man. Most people have seen what he's achieved in his career so far and his level of talent.
"We're looking forward to developing that even further. Making him even better. He's done so much all ready and what excites us is how far he can go."
More to follow.