Griffin turned down a deal with Stoke last summer in favour of a move to Derby, only to return to the Britannia Stadium for £300,000 in January.
"I came back to a club that means a lot to me and to go up is the stuff dreams are made of."
Thousands of fans lined the streets of Stoke on Tuesday night for an open-top bus ride that celebrated the Potters' return to the top flight of English football after a 23-year absence.
"It's incredible" said Griffin, who started his career at the Victoria Ground, before returning to Stoke last season for two separate loan spells. "I was expecting a celebration but nothing on this scale."
The former Newcastle and Portsmouth full-back also said that gaining promotion with the Potters has been emotional.
"There's been a few tears, I'm not ashamed to say that," he added. "It's been an amazing experience."