The Czech playmaker is out of contract at the end of the season, but Gunners boss Arsene Wenger revealed at the weekend that he expects Rosicky to sign a new deal in the coming weeks.
The 33-year-old, who joined Arsenal from Borussia Dortmund in 2006, impressed when standing in for Mesut Ozil against Sunderland on Saturday.
Rosicky's time at the club has been hampered by a number of injuries, and he missed the entire 2008-09 season due to a hamstring tendon problem that almost ended his career.
But he is back in Wenger's plans and remains convinced he is at the right place to win silverware sooner rather than later.
"I always believed in it here at Arsenal and still do. I knew this club was the right place for me and I want to be here for as long as I can," Rosicky told the official Arsenal magazine.
"It is obviously very difficult to predict how long I can go on for, (but) I feel very good. I don't feel any different than in the past, I don't feel any change in myself.
"All I can say is that I still have a big passion to achieve things and that is really important.
"You must have that force, that drive to go on and achieve something and I definitely still have that.
"I was nearly out of the game because of injury, so I have a different approach now because I know it could end at any point. I just want to be successful with Arsenal.
"I won three titles in the Czech Republic before I left (Sparta Prague), I won the Bundesliga with Dortmund and I still believe I can do it here.
"I wouldn't stay here if I didn't believe.
"The idea of winning the (Premier) League and the Champions League really drives me forward, I love it."