The 20-year-old was at Cantley Park on Friday morning to complete the paperwork on the deal before training with his new team mates. He is eligible to feature in Saturday’s trip to Sheffield Wednesday.
Galbraith has been on the books at Old Trafford since 2017 after moving over from his native Northern Ireland.
He has been a regular for both the club’s U18s and U23s throughout his time and has made one senior appearance, coming off the bench in the Europa League against FC Astana.
Galbraith has already won two senior caps for Northern Ireland, having first made his debut two years ago against Luxembourg.
He scored for Manchester United U21s in their EFL Trophy clash with Rovers in the 2019/20 campaign, producing a powerfully-struck volley from 20 yards to win the tie.
He will wear the number 22 shirt during his time at the Keepmoat.