Chelsea beat the Gunners 2-1 at Wembley to book a showdown with either Everton or Manchester United and Dutchman Hiddink praised his team for coming from behind to claim the win. 
Theo Walcott had given Arsenal an early lead but Hiddink's men hit back with goals from Florent Malouda and then Drogba - who profited from poor goalkeeping from Lukasz Fabianski to score the decisive goal with five minutes left.
The Dutchman has always maintained he will leave Chelsea in May and he now has the chance to give his side the best departing gift of all, The FA Cup.
"It means a lot to the team but also to me. One of my dreams was to win the Cup Final," he said.
"We made some changes in midfield and from there we had more of a grip on the game. We had dropped too far deep but then we played a little higher up.
"From there on we managed well and we scored as a consequence. We deserved it after that sloppy opening. We were dominant and it was only a matter of time until we scored for a second time.
"I know the team now from the inside - one thing is that we can play and always react to set backs. I like that very much."
Drogba was the Blues' hero and Hiddink hailed the Ivorian for sealing the place in the May 30 Final.
"He is proving he is so dangerous and strong - he is so fit. You don't get many chances to score in England but he is being inefficient," Hiddink added.
Teams
Arsenal
21 Lukasz Fabianski, 2 Abou Diaby, 4 Cesc Fabregas (c), 5 Kolo Toure, 11 Robin Van Persie (23 Andrey Arshavin, 75), 14 Theo Walcott, 15 Denilson (8 Samir Nasri, 86), 18 Mikael Silvestre, 25 Emmanuel Adebayor (26 Nicklas Bendtner, 83), 27 Emmanuel Eboue, 40 Kieran Gibbs
Substitutes not used
12 Carlos Vela, 16 Aaron Ramsey, 17 Alex Song, 24 Vito Mannone
Chelsea
1 Petr Cech, 2 Branislav Ivanovic, 3 Ashley Cole, 5 Michael Essien, 8 Frank Lampard, 11 Didier Drogba, 13 Michael Ballack, 15 Florent Malouda, 26 John Terry (c), 33 Alex, 39 Nicolas Anelka (21 Salomon Kalou, 83)
Substitutes not used
40 Henrique Hilario, 6 Ricardo Carvalho, 9 Franco Di Santo, 12 Jon Obi Mikel, 35 Juliano Belletti, 42 Michael Mancienne
Attendance
88,103
14 years ago