The first leg had finished goalless, and the second leg at the Hillsborough Stadium on Wednesday evening ended 1-1.
Mooy, who was outstanding yet again for Huddersfield, converted his penalty in the shootout.
READING FC will take on Huddersfield Town in the Championship play-off final after the Terriers edged past Sheffield Wednesday tonight (Wednesday).
Huddersfield will play Reading in the playoff final at Wembley Stadium on May 29 for what is the richest single game in soccer, potentially worth about 200 million pounds ($260 million) in future earnings to the winning side.
"Most pundits said before the season we would be in relegation trouble or maybe get relegated, and now we are only one step away from the Premier League".
Wagner said: "I'm happy and proud of what my players have done today and over the whole season".
Polls open with Iranians to give verdict on Rouhani
They dip one of their index fingers in ink, making a print on the form, while officials stamp their ID so they can't vote twice. The Guardian Council rejected Ahmadinejad's bid to run again in Friday's election, likely to avoid any similar conflict.
We'll have another look at some more specific odds a bit closer to the day but there you go, for now you can double your money if you think we'll be celebrating at the end of the day.
Both teams had chances to win it in extra time but Ward saved well from Jordan Rhodes and Wells fired into the side netting after a mis-hit-shot broke to him.
It was Wednesday's Fernando Forestieri who sealed Huddersfield's place in the final when he missed the decisive spot-kick, much to the dismay of the home crowd.
"One season is not easy to put the team in the play-offs and to do it twice is much more hard because of expectations, and I think we did well this season again".
We asked three dedicated supporters - one from Reading and two from Huddersfield - for their views.
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