The Bundesliga side guarded their 4-1 first-leg advantage for the majority of Tuesday’s second encounter at the Bernabeu, but late goals from Karim Benzema and Sergio Ramos nearly derailed their progress in devastating fashion.
But Dortmund are no strangers to a last-minute spectacle after ousting Malaga in the previous round with two goals in injury time, and with another dramatic triumph under their belts, Hummels took time to savour the achievement.
"I cannot believe it, this is unbelievable, it's what everyone in our team dreamed of as a child, and some of us are still children,” the German international told ITV.
"They scored a goal, they were refreshed and the crowd got louder when they scored. The second half, we had the game under control, but with [Benzema’s] goal, the game changed as it did against Malaga.
“It really is unbelievable what we've [achieved] this year, and now we're looking forward to [the final at] Wembley."
Midfielder Kevin Grosskreutz, who was called into action early in the first half to replace the injured Mario Gotze was also in a celebratory mood, maintaining that his team were deserving of their place in the final.
“They put a lot of pressure on us and scored two late goals. However we are a great club and deserved to go through,” explained the 24-year-old.
“I haven’t thought about Wembley yet, let's celebrate now and think about the final tomorrow."
Goalkeeper Roman Weidenfeller also extended his tributes to his side’s performance, highlighting their resilience as key to their eventual triumph.
“Real created enormous pressure in the beginning and at the end. They put all their eggs in one basket , but we stood up to it. Compliments to the whole team, we fought well and we deserved to progress,” said the Dortmund No. 1.
The showpiece event will take place at Wembley on May 25, and Dortmund may well be joined by Bundesliga rivals Bayern Munich, who hold a 4-0 first-leg lead over Barcelona in the other semi-final tie.