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Leicester, trailing 2-1 after winning the first leg 1-0, looked poised to reach the final when they were awarded a penalty in the 90th minute but Watford goalkeeper Manuel Almunia made a brilliant double save to deny Anthony Knockaert.
Watford broke quickly upfield and 20 seconds after the penalty save Deeney smashed the ball past Kasper Schmeichel to put Gianfranco Zola's team within one match of a return to the Premier League.
"I knew we had at least two minutes to score a goal but it was still important (to save the penalty)," former Arsenal ‘keeper Almunia told Sky Sports.
"I was lucky. We put all our efforts into scoring the last goal - it's unbelievable. It's the kind of game you always dream of being there and sometimes you're lucky enough to be on the pitch.
"We have to enjoy the moment, playing at Wembley - we won't play many times at Wembley so we have to enjoy it."
Watford, who missed out on automatic promotion to Hull City on the final day of the regular season, took the lead after 15 minutes when striker Matej Vydra fired home a brilliant angled volley.
But Leicester struck back four minutes later, David Nugent heading in a corner from close range.
Watford created more clear-cut chances and were rewarded after 65 minutes when Czech Vydra exchanged passes with Deeney and finished calmly.
The match appeared to be heading for extra time before the dramatic finale and Deeney's goal which ended Leicester's hopes of returning to the top flight after an absence of nine years.
Brighton and Hove Albion host Crystal Palace in the second Championship (second tier) playoff semi-final on Monday. The first leg ended 0-0.
The final is at Wembley on May 27.
Champions Cardiff City and Hull won automatic promotion to the Premier League.
