Ivan Toney and Emiliano Marcondes struck in the first half at Wembley to seal Brentford a place in the English top-flight for the first time since 1947.
It was redemption for Brentford boss Thomas Frank after his side lost last season's playoff final to Fulham. The result will earn Brentford something in the region of £170 million in Premier League income.
Brentford finally enjoyed playoff success after failing in their last nine attempts while Swansea were unable to return to the Premier League since relegation in 2018.
Swansea's miserable day was compounded when Jay Fulton was shown a straight red card in the second half for a poor challenge.
"It's crazy," said Toney, who failed to make the breakthrough at Newcastle United and spent much of his career out on loan.
"We were the better side even when they had 11 men and they didn't create any chances. We fully deserved it. I'm in the Premier League with the best bunch of boys."
Brentford were awarded a penalty inside the opening 10 minutes after Swansea goalkeeper Freddie Woodman brought down Bryan Mbeumo inside the box.
Toney converted from the spot to put Brentford ahead and score his 33rd goal of the season.
Brentford doubled their lead 10 minutes later after a swift counterattack saw Marcondes get on the end of Mads Roerslev's cross.
The Londoners almost grabbed a third moments later but Toney's stunning long-range volley struck the inside of the bar and bounced clear.
Swansea's best chance came on the stroke of half time when Andre Ayew's header clipped the crossbar.
Ayew had an even better chance after the break but he failed to guide his close-range header towards goal.
Swansea continued to press forward and came close once more after the hour mark when Jamal Lowe's shot went just wide.
However, their chances of a fightback took a massive blow five minutes later when Fulton was sent off for a reckless challenge on Mathias Jensen.
Despite some late Swansea pressure, Brentford held on for the win and booked their place into the Premier League.
The final whistle sparked jubilation for Frank and his players and offered conclusive proof of the methods of club owner Matthew Benham -- a former professional gambler who employed the deep statistical analysis of data that earned him millions to great effect to transform a club which has lived in the shadows of the capital's giants.
Toney is a prime example of Brentford's "Moneyball" transfer policy. He was signed for £5m last year from Peterborough to replace Ollie Watkins who joined Aston Villa for £33m, having arrived for £1.8m.
"Right now I'm empty," Frank said. "I don't know how to describe it. Last season I thought we deserved to go up but we didn't and that's football. This group of players is incredible.
"Everyone made a major part in this. I think we have been one of the best teams in the past two years."
Information from Reuters was included in this report.