It is the first time in 84 years that Hull have reached this stage of the competition.
Three goals in 10 second-half minutes saw Sunderland beaten 3-0 at the KC Stadium and booked the clash against the Blades, with whom Bruce began his managerial career in a brief stint starting in 1998.
Bruce said: "Sheffield United gave me my chance in management a long, long time ago.
"I'm delighted for everyone. I've seen the scenes at Bramall Lane today and now we've got a big Yorkshire derby to look forward to at Wembley, which will be a magnificent occasion for everyone."
The Tigers' second-half spree set light to a largely dismal clash with Gus Poyet's men, who were clearly suffering a hangover after their heroic performance in last weekend's Capital One Cup final against Manchester City.
Clearly with one eye on a Barclays Premier League relegation battle, Poyet made six changes and saw his side struggle to stay in touch with the hosts, only reaching half-time level due to keeper Oscar Ustari's 33rd-minute penalty save from Sone Aluko.
Otherwise the first period was only notable for the antics of Black Cats midfielder Lee Cattermole, who was booked after tangling with both Ahmed Elmohamady and David Meyler, and whose afternoon would go from bad to worse.
Tigers captain Curtis Davies headed his side into a 68th-minute lead from a Tom Huddlestone free-kick, and four minutes later Meyler blazed past Cattermole to get on the end of George Boyd's long punt upfield and slot past Ustari.
Sunderland's misery was complete when Cattermole's dismal back-pass let in Matty Fryatt to seal the home side's win and their historic trip to Wembley.
While Poyet was clearly relieved at being able to focus on the survival fight ahead he also refused to pin any blame on Cattermole for his side's abject showing.
Poyet said: "If you hide and you're not in the game and do nothing to take a risk, then for sure you're not going to make any (mistakes).
"That's the bad side of football - the ones that take responsibility and the ones that care, they are the ones who are in the position to make the mistakes - that's football."
Meanwhile Bruce picked out Meyler for special praise after the former Sunderland midfielder marked his goal with a joke head-butt against the corner flag - a reference to his high-profile spat with Newcastle boss Alan Pardew last week.
Bruce said: "In the way he has conducted and handled himself this week David has been a model for me.
"David took it on the chin and accepted the apology. He didn't roll on the floor and he didn't go and bleat in the newspapers.
"He's had two horrible injuries and he's a former Sunderland player. He's chased something you would not expect him to get to but his determination and attitude has made him a firm favourite here."