Steve Cooper's Forest side will host the first leg against United after beating Wolverhampton Wanderers 4-3 in a penalty shootout on Wednesday following a 1-1 draw
Southampton, bottom of the Premier League, stunned Manchester City 2-0 to reach the last four.
The two legs will be played in the weeks commencing 23 and 30 January.
Manchester United secured their place in the semi-finals by beating League One Charlton 3-0 at Old Trafford on Tuesday.
They have won the EFL Cup five times, most recently in 2017, and beat Forest in the final back in 1992.
Newcastle, who are third in the Premier League, beat Leicester 2-0 to progress to the last four
EFL Cup draw:
Nottingham Forest v Manchester United
Southampton v Newcastle
