The Hatters secured a fourth promotion in 10 seasons, 6-5, in the shootout after the teams were tied at 1-1 after 120 minutes.
Financial experts estimate promotion to world soccer's most watched league to be worth around £170 million ($210 million) for a club that have been through turmoil since it last played in the top flight 31 years ago.
Luton are the first club to go from the fifth tier to the top flight in the Premier League era.
Midfielder Pelly Ruddock Mpanzu has been on that whole journey and becomes the first player to go from the National League to Premier League with the same club.
"I feel like I completed football," said Mpanzu. "It's been a journey. It's going to be a party all summer."
Some of Luton's cash windfall will go to upgrading the club's stadium, Kenilworth Road, which with a capacity just over 10,000 and set among rows of terraced houses, will be hosting the likes of Manchester United and Liverpool next season.
Luton had to recover from an early shock when captain Tom Lockyer collapsed on the field.
The Welsh center-back was stretchered off and taken to hospital, where the club confirmed he was responsive and able to talk to his family.
"I feel really good, but the only thing I'm thinking about now is Tom Lockyer," said Luton manager Rob Edwards.
Lockyer had played his part when Luton had the ball in the net after just five minutes when Gabriel Osho was flagged offside as he forced the ball in from close range.
But a bright start from Edwards' men was rewarded on 23 minutes when Elijah Adebayo's good work down the left teed up Jordan Clark to smash home at the near post.
Adebayo had a second Luton goal ruled out before halftime for handball.
Coventry looked like a team that had stage fright in front of 85,000 people in the first-half. But Mark Robins' side has grown used to thriving in adversity.
In the 22 years away from the top flight, Coventry has been forced out of its home city to Northampton and Birmingham due to financial issues in leasing its stadium.
Even when restored to Coventry, it began the season at the foot of the Championship standings after being unable to host home games due to the state of the field which had been used for rugby at the Commonwealth Games.
Coventry were much improved after the break and got its reward 24 minutes from time when Viktor Gyokeres teed up Gustavo Hamer to fire into the far corner.
The Sky Blues nearly turned the tie around fully within minutes when Matt Godden blazed a big chance over.
Tired legs and tension took over in extra-time, but Coventry had a massive let off four minutes from time.
Joe Taylor slotted home after charging down Jonathan Panzo's clearance, but the goal was ruled out as the ball struck the Luton man's hand.
All of the first 11 penalties were then scored as the takers showed incredible poise under the most extreme pressure.
But when Fankaty Dabo's effort sailed over the bar of American Ethan Horvath's goal, Luton's dreams came true.
© Agence France-Presse