He joins a Rams side siting 16th in the second tier, but Rooney believes he can still cut in the top division.
"Now my ambition is to get Derby back in the Premier League and hopefully play my part there for them.
"Ryan Giggs was able to play into his late thirties in the Premier League and Gareth Barry says he wants to do it at 40.
"Given the right team around me, then I could still play in the Premier League."
Rooney plans to go into management in the future, but believes he still has a lot to offer on the pitch if teams play to his strengths.
"It's important to understand football. It is not all about running round, it is about using your head to play the game," he explained.
"Sometimes that gets lost, because you don't score as many goals or whatever.
"The two teams I played for in the Premier League were Manchester United and Everton. I am at Derby now, and hopefully we can get there with them."
The 34-year-old had been playing in the USA with DC United, where he scored an impressive 23 goals in 48 outings for the capital side.
He will join up with the Rams on an 18-month contract, though he had two seasons left on his deal with the MLS outfit.
Derby chairman proclaimed at the time the signing was announced, back in August, that Rooney will be joining the club primarily as a player.
With his deal set to begin in January, Rooney's debut could come at Pride Park against Barnsley on January 2. Before then, they travel to Reading and Wigan then host Charlton.