Goals from Anwar El Ghazi and John McGinn put Villa 2-0 up before Martyn Waghorn pulled one back for Derby in the 81st minute, but Dean Smith's side held on for the victory under intense pressure.
The playoff final is considered the most lucrative single game of football in the world, with promotion earning Villa an estimated 170 million pounds ($215.51 million) in revenue.
Norwich City and Sheffield United had already secured promotion to the top flight for next season after finishing in the top two positions in the second tier Championship.
Villa, European champions in 1982, were relegated in 2016 and lost to Fulham in last year's playoff final.
El Ghazi opened the scoring just before the break with a diving header from Ahmed Elmohamady's cross from the right.
McGinn doubled the advantage in the 59th minute when a deflected shot from El Ghazi looped into the area. Derby keeper Kelle Roos came out but was unable to capture the ball under a challenge from McGinn, who bundled it home.
Derby, managed by former Chelsea and England midfielder Frank Lampard, got back in the game when substitute Jack Marriott's low shot was turned in by Waghorn and they piled on the pressure in the final minutes, but were unable to break through.
Villa's local-born midfielder Jack Grealish, who was close to leaving the club before the start of the season, showed his class throughout and was delighted with promotion.
"I'm speechless. It was such a hard game... It means the world to go up, we know where this club belongs. I've stayed here and we're back there now. I've led my boyhood team to the Premier League," he said.
A 10-match winning streak during the run-in propelled Smith’s Villa side into the playoffs where they got past West Midlands rivals West Bromwich Albion in the semi-finals.
Smith, who began the season at Brentford and took over from Steve Bruce at Villa Park in October, said the club had an exciting future with the backing of owners Nassef Sawiris and Wes Edens.
"It feels very good. The lads are a terrific bunch. They take on different ideas, they deserve it. I believe pressure is what you put on yourself, we work hard every day, the only difference is expectation. We've got two owners have got a lot of money, and are in it for the long haul. The potential now is massive," he said.
(Reporting by Simon Evans, editing by Pritha Sarkar and Toby Davis)
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