Saturday's Sky Bet Championship play-off final went the distance at a packed Wembley, where the Hatters rallied after their skipper's worryingly collapse early on.
Jordan Clark put Luton into a deserved lead that Coventry midfielder Gustavo Hamer cancelled out in the second half, with the match ending 1-1 after 90 minutes and extra-time.
Joe Taylor saw a winner ruled out just before spot-kicks, with Fankaty Dabo's sudden-death miss sealing a 6-5 shoot-out triumph that propelled Luton back into the top-flight for the first time since 1992.
The dramatic triumph means the Hatters will welcome Manchester City and Co just nine years after facing the likes of Salisbury and Hyde in the Conference Premier.
Luton boss Edwards said: "I felt a bit numb. I just made sure I shook Mark's hand and his staff.
"I don't want to be that guy that just starts running off and celebrating before I've seen the other manager.
"I just felt very numb. I still do. It hasn't sunk in quite yet. It might take a few days, but it's great. It does feel good.
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