The English midfielder has been a key asset to the Cottagers' promotion charge this season, scoring the winner in the final to lead his team to the Premier League.
Fulham will return to the top flight of English football for the first time in four years, and Cairney is delighted with the direction that the club is heading.
"It feels incredible, it feels like an out-of-body feeling," Cairney told Sky Sports News.
"I swear, in that last minute when the ref blew the whistle and we were defending with 10 men for 20 minutes, I had a feeling they wouldn't score. It was our time, it was going to be our year. It's a dream come true. For the last year, 18 months or so I've been linked with a few clubs and people have been questioning what I was doing, but I've signed a contract extension for a reason.
"I believe what we're doing here is special, what the gaffer is doing is special. I've said for quite a while we've been playing Premier League football in the Championship and I'm so happy we get to play Premier League football in the Premier League. When we didn't get promotion at the end of the season, a lot of people wrote us off and said we had to change the way we play. People gave us stick but football won today."
Fulham will join Wolverhampton Wanderers and Cardiff City in the Premier League next campaign.