Forest defeated Huddersfield Town 1-0 in the Championship play-off final at Wembley on Sunday.
Levi Colwill's own goal ensured that the two-time European champions will be back among the big boys for the first time since the 1998/1999 season.
It has been a major turnaround for a Nottingham Forest side who were bottom of the Championship table when Cooper took over in September last year, and the former England u-17 manager has expressed delight at his achievement.
Cooper told Sky Sports: "I'm really pleased for the players and the supporters. I think we played well in the first half. And of all the good goals we've scored this season, we get one like that - but it doesn't matter. And we managed to see it through. Everyone connected to this football club deserves this today. We're looking forward to a positive future.
"It's relief of course but it's pride. I love being at this football club. It's changed my life. My family are here, the players' families are here - this football club is about belonging to a city. It comes together on matchday. We've taken over Wembley today and are in the Premier League.
"This football club is built on positive eras from the past and we want to build on that. We are proud of that but at the same time we need to think 'what if?' Can we get the Premier League? Can we play attractive football? What if we can develop young players? And that's what we've done showing an attitude and a commitment to not get beat. We deserve this.
"It's a glamorous world being a footballer and a manager but it's also a a harsh and spiteful one. And I just wanted the players to know I will be their biggest supporter and give them everything through thick and thin. It doesn't mean I'm soft with them or don't demand of them but everybody loves to be loved. That's what we've tried to do with the players."
