Jordan Rhodes’ solitary late goal clinched the Terriers a 1-0 second-leg victory at the John Smith’s Stadium and a 2-1 aggregate triumph.
Corberan, in his second season in charge, said: “We knew that having the right mentality and the right character was going to be important if we wanted to reach Wembley.
“First of all, I must congratulate the players and I’m looking forward to the final.
“Nothing makes me feel more proud than seeing how happy they are and how much they identify with the team.
“We’ll rest in the next couple of days and then we will start working towards that game and see who we are going to play.”
The victory sparked remarkable celebrations at the John Smith's Stadium, with fans rushing onto the pitch to mark their side's triumph in the play-off semi-finals.
Can you spot yourself in any of these pictures?