Jose Mourinho's men required a stoppage-time victor from Marcus Rashford earlier this season to see off the Tigers, who reached a first League Cup semi-final in club history by beating Newcastle United on penalties on Tuesday.
The first leg of the semi-final will be played in the week commencing 9th January.
Ticket details for both legs will be announced in due course once they have been finalised.
The Irons picked up a 1-1 draw against the Red Devils in a Premier League fixture on Sunday with Diafra Sakho's second-minute goal being cancelled out by a Zlatan Ibrahimovic header in the 21st minute.
Elsewhere in the final-four draw, Southampton will face Liverpool over two legs following the completion of tonight's quarter-finals.
Jose Mourinho's men host the Tigers first at Old Trafford before heading to the KCOM Stadium. "I told them to forget about the undeserved goal, we are playing so well, we have to keep the confidence and lets go on with it. Goals plus performance means the real happiness".
Manchester United will face Hull City in the next round, while Southampton face Liverpool. Their opponents Hull defeated Newcastle in a penalty shootout to reach the semis.
"Manchester United were at Wembley last season".
Hull's progress to the last four will mean that they will play at least 12 games in a busy seven week spell, with the possibility of another addition if they are involved in an FA Cup third-round replay next month.
In the other quarterfinal match on Wednesday, Southampton beat a largely second-string Arsenal team 2-0 thanks to first-half goals by Jordy Clasie and Ryan Bertrand at Emirates Stadium.