Hull defeated Premier League rivals Sunderland 3-0 in their quarter-final tie at the KC Stadium to set up a meeting with third-tier United, who had earlier overcome Charlton Athletic 2-0 to reach the last four.
Arsenal, meanwhile, will face City in the semi-finals if Manuel Pellegrini's side can overcome Wigan Athletic later on Sunday, when they will be seeking to avenge their shock defeat in last season's final.
Hull squandered an opportunity to take the lead in the first half against Sunderland when Sone Aluko saw a penalty saved by Oscar Ustari, but Steve Bruce's side ran away with the game in the second period.
Curtis Davies broke the deadlock with a 68th-minute header and David Meyler made it 2-0 four minutes later, celebrating by headbutting the corner flag in a reference to his clash with Newcastle United manager Alan Pardew last weekend.
A blind back-pass by Lee Cattermole enabled Matty Fryatt to add a third in the 77th minute, further blackening Sunderland's mood following their 3-1 loss to City in last weekend's League Cup final.
The final whistle sparked a pitch invasion, with Hull's jubilant supporters pouring onto the playing surface to celebrate their team reaching the last four for the first time since 1930.
"I've just seen the draw and it's a great one," said Hull manager Bruce, who twice won the trophy as a player with Manchester United.
"Sheffield United have had a wonderful run and beaten every team put in front of them.
"But you have got to be honest -- you want to avoid the big boys and I'm sure Sheffield United will be thinking the same having drawn us."
Sheffield United continued their remarkable journey in the FA Cup by upsetting second-tier Charlton at Bramall Lane.
Managed by Nigel Clough, son of legendary former Nottingham Forest manager Brian, the Blades became the first team from the third tier to reach the last four since Wycombe Wanderers in 2001.
"I'm just delighted for everybody that we're going to Wembley, especially the players," Clough, whose late father never won the tournament, told BT Sport.
"To win nine games on the spin, they deserve an immense amount of credit
We hope to play a lot more big games like this in the future."
Having previously accounted for Premier League sides Fulham and Aston Villa, as well as second-tier Forest, the Blades prevailed thanks to quick-fire goals from Ryan Flynn and John Brayford mid-way through the second half.
Charlton winger Callum Harriott had just poked the ball wide of an open goal from a Marcus Tudgay cross when Flynn put the hosts in front in the 65th minute.
Former Everton trainee Jose Baxter swept an inviting cross into the penalty area from wide on the left and Flynn stole in at the back post to prod the ball home with the studs of his right boot.
Brayford's deflected shot made it 2-0 to the League One club just two minutes later, leaving United's fans to savour the prospect of a semi-final date with Hull next month.
Source : AFP