Brown told Sky Sports 1: "It's marvellous - I feel for the Bristol City lads - but it is very fitting that Dean Windass got the winning goal.
"I think it was written in the gods that it would be Dean Windass or Nicky Barmby who would get the winner. The players have tried hard all season and thoroughly deserve it. It is fantastic feeling to do it here in front of all of these supporters."
Windass said: "It feels unbelievable. I don't think there is anyone left in Hull today looking at how many supporters we've got here. To score the wining goal is fantastic. We've worked hard from the start of the season and we've got our rewards for that."
Fellow Hull-born forward Barmby added: "It is amazing to have done it with my hometown club, who have never been in the Premier League.
"It means everything for the kids in the city to see Premier League football and I'm absolutely delighted."
Robins boss Gary Johnson said: "I didn't want to be making the losing speech but unfortunately I am.
"We got beaten 1-0 and all I can say is well done to Hull. They are up in the Premier League. We have to work a bit harder to get there."