Leeds captain Ethan Ampadu said Premier League promotion felt "amazing" and said the club will now target securing the Championship title.
The Whites thrashed Stoke 6-0 at Elland Road to remain top of the table and the players then stayed to watch Burnley's 2-1 win over Sheffield United at Turf Moor, which confirmed promotion for both Leeds and the Clarets.
Leeds fans gathered outside the ground in their thousands to celebrate their top-flight return.
Ampadu said: "It's amazing. If you look at the scenes here, as it was after the final whistle, just pure excitement.
"Within ourselves we've got another target, so we can enjoy this now, but we've got another target we want to achieve. But right now, it's very good."
Joel Piroe grabbed four goals for Leeds against hapless Stoke, including the club's fastest ever league hat-trick with strikes in the sixth, eighth and 20th minutes. He added his fourth before half-time after Junior Firpo had put Daniel Farke's side 4-0 up in 26 minutes.
Willy Gnonto headed the hosts' sixth in the second half to help seal Leeds' Premier League return after a two-year absence.
Leeds came up short during last season's run-in, dropping out of the top two before losing to Southampton in the play-off final, and Ampadu said that heartache had helped fuel Farke's side this time round.
"Definitely. The lads that were here last year - we all felt that hurt," he said.
"After the game at Wembley we wanted to put it right straightaway and we've had to wait another season. The lads who came in have been excellent, joining in with what we wanted to achieve.
"Thankfully one part is done. Everyone knows what the next part is, but it's fantastic."
Ampadu's Wales team-mate Joe Rodon said he was "buzzing" for everyone involved with the Elland Road club.
Rodon said: "For me it hasn't sunk in yet. I don't think it will until the end of the season, but I'm just delighted for everyone involved with the club, the fans and what it means to them.
"It's what everyone has worked for all season and I'm buzzing.
"(Last season) didn't sit right with me. The boys who have come in have been brilliant and we set out to do what we've done. I'm just delighted for everyone."
Leeds boss Farke, who won promotion to the Premier League twice with Norwich in 2019 and 2021, said he was "lost for words".
Farke, enjoying a celebratory beer, said: "It doesn't happen that often.
"You can see the atmosphere here, it's incredible. It's well deserved, 94 points at this stage is unbelievable. The lads should celebrate, all our supporters should celebrate.
"It's difficult on such an emotional day to reflect too much, but it was a long road. It's not easy to stabilise the ship after relegation and to deal with that.
"We played fantastic last season, with 90 minutes, before the heart-breaking game at Wembley, but to show resilience and keep going, we deserve today to celebrate."
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