The Bantams lost 2-1 in their second leg at Villa Park, but become the first fourth tier side to reach the League Cup final since Rochdale in 1962 thanks to their 3-1 first leg win over their Premier League opponents a fortnight ago.
Christian Benteke had given Villa a first half lead before Hanson levelled the scores early in the second half. And a late Andreas Weimann effort resulted in a nervous finale but the Bantams held on to reach Wembley where they will face either Swansea or Chelsea.
Villa almost went ahead on six minutes when Matt Lowton got on the end of a Benteke flick on to head just over from close range, before Benteke headed straight at Matt Duke from six yards on 16 minutes.
Fabian Delph lashed a strike over the bar and Gabby Agbonlahor's turn and shot in the Bradford box was straight at Duke.
However, Villa took the lead on 24 minutes when Joe Bennett's excellent cross from the left was met by Benteke in the centre and the Belgian hitman coolly volleyed into the net from close range.
Stephen Ireland had the ball in the net moments later following more good play by Bennett but the offside flag denied him, while Charles N'Zogbia's fierce drive was tipped over by Duke on 32 minutes.
Villa continued to press for the second goal that would have tied the game at 3-3 on aggregate before the interval but Ireland's delicate chip was tipped over by Duke on 38 minutes, before Benteke bundled the ball past the back post.
After all of Villa's attacking play, Bradford could have equalised on the night in first half stoppage time. Nahki Wells picked up the ball just outside the area and curled a strike inches wide of Shay Given's far post.
Villa started the second half brightly with Benteke again heading just wide on 47 minutes, but Bradford exploited Villa's inability to defend set-pieces on 55 minutes as Hanson powered in a header from a Gary Jones corner.
Villa boss Paul Lambert then had all of his attacking players on the pitch in search of a way back into the contest.
And, when Weimann got on the end of a Darren Bent flick on and went around Duke to make it 2-1 in the 89th minute, the Villa fans had some hope that their side could grab a third and take the tie to extra time.
But Bradford held on through four minutes of stoppage time to record one of the biggest cup stories of all time and seal their place in the history books.