The 21-year-old will stay on loan at Gigg Lane until the end of the season, after the deal gained clearance from the Premier League.
“We have signed him now and he is available to play for us at the weekend [against Bradford],” Shakers boss Alan Knill told Sky Sports.
“He will firstly bring us more competition for places, which I feel we have been lacking in recent weeks.
“However, he is also a really good footballer that can play in a variety of attacking positions, in the centre or on the left or right as well as just behind the strikers, so he will give us a lot more options in terms of team shape.”
