The Seagulls achieved the feat with a 2-1 win over Wigan on Tuesday that saw them go seven points clear at the Championship summit with three matches left.
And when Aaron Mooy's Hudderfsield Town were held 1-1 by Derby County, Brighton's move to the topflight was assured.
Brighton, who last played in the old First Division in 1982/83, narrowly missed out on top-flight football a year ago when they finished third following a 1-1 draw with Middlesbrough on the final day of the season, eventually succumbing in the play-off semi-finals.
"It's a wonderful achievement and there's so many people that I'm absolutely delighted for, certainly the chairman [Tony Bloom]. He's a local man and has invested an incredible amount of money in this football club," Hughton said after the match at Amex Stadium.
"I knew we had a group of lads that were capable of doing it, but being capable of doing it and actually doing it are two different things.
"They've been good all season. They've bounced back and shown good determination and desire to win as many games as possible.
"Right at this moment, this is the most exciting one [achievement]. I went up with Newcastle as a team that just came down, and although we'd lost players, I had a very strong team.
"This is a club that haven't been in the Premier League. This was a club that had been in the play-offs two years running before I got here, so it wasn't a club that was used to being at the bottom end of the division."