The 16-year-old made history in May 2016 when he became the first player born in the 21st century to feature in a Football League fixture.
Styles, born in March 2000, arrived at Gigg Lane in March 2016 after being released by Burnley and made his debut from the bench in a 3-2 victory over Southend United in the final game of last season.
"He is an unbelievable talent and a very special player," new Shakers manager Lee Clark told the club website. "I saw him when he came on to the pitch at Chesterfield [on Saturday], and he was awesome."
Styles's new deal at Bury will run until the summer of 2019.