The German will team up with long-time karting friend Hamilton at the Brackley-based squad after the latter decided to leave McLaren.
There have been speculation that Hamilton would get the number one status at Merc, but team principal Ross Brawn has already dismissed the reports while Rosberg is ready for any challenge that comes his way.
"No, absolutely not," he told German newspaper Bild am Sonntag.
"I know the situation. For three years I had Michael, one of the fastest in the world, with me. I have always been comfortable with that.
"Lewis coming here is a challenge and I gladly accept. Lewis is one of the best drivers at the moment but I believe I can measure up."
As for claims in the press that Hamilton joined Mercedes with the belief that he would be given number one status at the team, Rosberg - and previously Ross Brawn - denied this.
"I have it written in my contract that I will always have the same opportunities as my team-mate - no matter who that is."
Pressed as to whether he had concerns about his relationship with Hamilton ending up like the Brit's with Fernando Alonso at McLaren in 2007, Rosberg said: "Both of us are smart enough that it won't degenerate."
Asked if he felt any "pity" for Schumacher given that he has lost his race-seat, Rosberg said with a laugh: "No, sorry I don't.
"He was unsure whether he wanted to continue so Mercedes were forced to choose. Michael has already said himself that he's not unhappy."