Borthwick-Jackson played 14 times for United's senior side last season but has found himself further down the pecking order at Old Trafford given the return of Luke Shaw from injury.
The 19-year-old has represented England at U-19 level in the past.
Ola John has joined on loan from Benfica. Unlike Borthwick-Jackson, this will be John's second Championship loan spell, after spending last season on loan at Reading.
The winger is a full Netherlands international, having won one cap for his country.