Scunthorpe wanted the defender to replace Conor Townsend who is close to signing a deal with West Brom.
Borthwick-Jackson spent last season on loan to Leeds, but only made six appearances in all competitions.
He told the League 1 team's website: "I’ve been at Manchester United since I was six years old and I’ve progressed all the way through."
"I managed to get my opportunity in the first team in the 2015/16 season, that was a great season for me and kick-started my career."
"I know it’ll be more a lot more physical in League One, so I’ll have to see how I adapt to that and hopefully I can impress."
The 21-year-old defender made his debut under former-Manchester United boss Louis van Gaal, but failed to make an impact under Mourinho.