Kelly prodded the ball past Merle Frohms in the 110th minute to restore the tournament hosts' lead after fellow substitute Ella Toone's wonderful lobbed opener just after the hour mark.
Eight-time champions Germany - who had lost star forward Alexandra Popp to injury in the warm-up - equalised with 11 minutes of normal time remaining through Lina Magull, and the game looked on course for a penalty shootout until Kelly's effort fired Sarina Wiegman's side to glory.
A year on from the men's team losing their Euros final at the stadium on penalties to Italy, England can celebrate the first piece of major silverware for a senior side since the men's 1966 World Cup triumph over West Germany.
And there was jubilation at the final whistle as the players tried to take in what they had done amid an almighty roar from the 87,192 crowd - the biggest-ever attendance for any Euros match, men's or women's.
Meanwhile, boss Wiegman could savour back-to-back Euros successes after overseeing the Netherlands' triumph on home soil in 2017. Her record in charge of England after taking up her post last September has been near-flawless - 20 games, no defeats, 18 wins, 106 goals scored and only five conceded.
It was a third appearance in a Euros final for the team, and first since losing 6-2 to Germany at Euro 2009 in Finland.
The English women's game has been on a journey of considerable growth in the intervening years, with the sense of momentum certainly apparent over the last few weeks as Wiegman's team have thrilled large stadium crowds and television audiences - and there will be sky-high hopes for what the future holds after this historic moment.
There was also a personal triumph for Beth Mead, who claimed the Golden Boot after finishing the tournament with six goals - the same amount as Popp, with Mead taking the prize due to her superior assists tally.
