Thomas Frank’s side completed their fairytale rise thanks to first-half goals from Ivan Toney and Emiliano Marcondes at Wembley.
Swansea’s Jay Fulton was sent off midway through the second half to put the result beyond doubt in what is widely regarded as football’s single most lucrative game.
After decades stuck in lower league obscurity, unfashionable Brentford will be one of the smallest clubs ever to play in the top tier.
In just their second season at the new Brentford Community Stadium, the Bees will welcome the likes of Manchester City, Manchester United and Liverpool to west London.
The riches earned from the victory will be transformative for Brentford, who have finally erased the painful memories of their wretched play-off past.
Beaten by Fulham in last season’s Championship final, Brentford had failed to earn promotion in all nine of their play-off appearances before this term.
No team had lost more play-off finals than Brentford’s four, but Frank had insisted the bad omens would count for nothing.
The Bees boss was proved right as he became the first Danish coach to win a Football League promotion.
“It’s unbelievable, I’m so proud,” Brentford’s Swedish captain Pontus Jansson said.
“It’s been a hard year but we’re finally there. This year we had a very strong group and we believed in it from day one.”
Brentford’s rise has captured the imagination of neutrals after they spent 59 out of 60 seasons in the third or fourth tiers before reaching the Championship in 2014.
They have climbed well above their traditional status thanks to innovative owner Matthew Benham.
Benham has introduced an analytics-influenced approach overseen by two directors of football, ensuring the club make the most of their resources, which are meagre in comparison with the Championship’s wealthier teams.
Fittingly, it was Championship top scorer Toney who put Brentford on course for the top-flight for the first time since 1947.
Toney, signed from third tier Peterborough last year, fired Brentford to a third-place finish despite the close-season sales of star forwards Ollie Watkins and Said Benrahma to Aston Villa and West Ham respectively.
Now the 25-year-old, rejected by Newcastle as a youngster, will get the chance to show he can thrive in the Premier League.
Six of Brentford’s team started last season’s final and they quickly seized the initiative in their bid for redemption.
In front of a crowd of 11,689, including with 5,000 fans admitted from each club following the easing of lockdown restrictions, Brentford took the lead in the 10th minute.
Bryan Mbeumo made a clever run behind the Swansea defence to reach Sergi Canos’s superb pass into the penalty area, prompting Freddie Woodman to race off his line and crash into the Brentford striker.
Referee Chris Kavanagh pointed to the spot and Toney stepped up to slot the penalty past Woodman for his 33rd goal of the season.
Brentford weren’t going to sit on their lead and a blistering counter-attack produced their second goal in the 20th minute.
Breaking from their own penalty area, Frank’s men caught Swansea out of position as Mbeumo picked out the over-lapping Mads Roerslev.
Roerslev’s cross was perfectly measured for Marcondes and he guided a clinical finish past Woodman from 12 yards.
Toney was inches away from his second goal moments later when his dipping volley hit the bar and bounced clear off the line.
Shell-shocked Swansea were so out of sorts they didn’t manage a single shot on target in the entire game.
And when Fulton saw red in the 65th minute for a crude foul on Mathias Jensen, it was only a matter of time before Brentford could start their promotion party. (AFP)