The 20-year-old, who was born in the city, has been in the club's youth system since 2002, and could make his first league appearance against City this weekend.
Blackett told the club's website: "I was brought up here in Manchester and playing now for United is like a dream come true. Hopefully, I'll continue to do my best for the club.
"Being a local lad, there's extra pressure but it's something I thrive on. As one of the more local lads, I know what this club means. Don't get me wrong, the foreign players know Manchester United as well but being a local lad gives you extra incentive to do well.
"I'm from Hulme, right in the city centre. There are City fans where I live and I get a bit of stick now and again but it's all good banter and good to be around it. There's a lot more of them now!"
Louis van Gaal's side face the Premier League champions at the Etihad Stadium on Sunday.