Byrne, who had a temporary spell with the npower League One side last season, has signed a two-year contract at Gigg Lane after the two clubs reached an agreement for the central midfielder.
The 19-year-old's stay with the Shakers was cut short by an ankle injury following 15 appearances.
Byrne signed his first professional contract with Leicester last summer but has been allowed to leave after failing to force his way into first-team contention.
He will go straight into the Bury squad for their game against Coventry on Saturday.
- Gigg Lane