Swansea's players expressed their joy after the 2-1 win at Gillingham took them to the league's second tier for the first time in 24 years.
"It's a privilege to lead the team, to go one down then win - well, we're going to enjoy ourselves after that," said captain-for-the-day Alan Tate.
"It's brilliant for the fans, the city, everyone - the town will be buzzing."
Two-goal hero Guillem Bauza added: "This is the best feeling I've ever had, it's all for the fans."
The win saw the Swans set a club record of 86 points, beating the 85 of John Hollins' 1999-2000 side.
They are seven points clear of second-placed Carlisle with three to play, and could clinch the League One title next Saturday.
"It's unbelievable," said Swans midfielder Leon Britton. "In the second half we fended off wave after wave of attacks from Gillingham.
"The supporters have been brilliant all season and they were again this time, they deserve this.
"Now we just want to get on and prove ourselves in the Championship."
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