Scott Sinclair fired a hat-trick and Stephen Dobbie also netted in the Championship play-off final as the Swans booked a top-flight spot after a 27-year wait.
Northern Irishman Rodgers saw his men storm into a 3-0 interval lead against his former side before Reading came roaring back through an own goal from Joe Allen and a Matthew Mills header.
Then Jem Karacan hit the post as Brian McDermott’s outfit almost completed an incredible second-half fightback in a compelling contest.
But Sinclair scored his second penalty of the game as Swansea became the first Welsh member of the Premier League, just eight years after the club were on the verge of dropping into the Conference.
Rodgers said: “I’m very proud. But it’s an ironic story as eight years ago the club won the last game of the season against Hull to stay in the league. Otherwise they would have dropped out of the division.
“They won that game 4-2, one player scored a hat-trick and scored two penalties.
“It’s ironic to become the first Welsh side in the Premier League so the footballing gods were with us.
“But, over the course of the season, I don’t think anyone can take this opportunity away from us.
“We won the game with moments of quality and deserved to win.”
Rodgers, who hails from the village of Carnlough in County Antrim, clinched promotion in his first full season at the Liberty Stadium after short, yet ill-fated spells at Reading and Watford.
But the ex-Royals manager, who was sacked after just 21 games at the Madjeski Stadium, admitted the showpiece final had been an emotional rollercoaster.
Rodgers added: “It was a funny sort of day. My professional head was to do the job for Swansea.
“They have really accepted me into their lives as players and people. My connection with Reading was a strange one but I will never say a bad word about them.
“I said to the players at half-time that this game is nowhere near being over. Against most teams at 3-0, it would be over but not Reading.
“I knew over 50% of their goals came from crosses and set-pieces so it was no surprise.
“They were difficult to stop, but at 3-2 we were able to refocus in the game.”
Rodgers now joins Wolverhampton Wanderers chief Mick McCarthy as the Irish managerial representation in the Premier League.
But the 38-year-old admits he will relish the challenge of pitting his wits against the best managers in the top tier of English football.
Rodgers added: “I saw a great Northern Ireland flag out there which said Brendan Rodgers on it. I have always said I am representing Wales but also Ireland.
“I have seen my family and it’s important we celebrate success and moments like this together. We’ll all go back to Swansea and celebrate with the supporters and people in the city. It’s a great achievement and I’ll enjoy the next few days.
“Then I will look at the next chapter and next season.”
READING: Federici, Griffin (Robson-Kanu 84), Mills, Khizanishvili, Harte, Kebe, Karacan, Leigertwood, McAnuff, Long, Hunt (Church 76).
SWANSEA: De Vries, Rangel, Monk, Williams, Tate, Dyer, Britton (Gower 77), Dobbie (Pratley 55), Allen (Moore 89), Sinclair, Borini.
Ref: Phil Dowd (Staffordshire).