Rosicky replaced Mesut Ozil in Arsenal's side on Saturday and proved a worthy understudy, adding a stylish third goal in a 4-1 thrashing of Sunderland.
The Czech playmaker has been hampered by a string of injuries since joining Arsenal from Borussia Dortmund in 2006 and the 33-year-old is yet to extend his current deal, which expires in the summer.
But Wenger insists Rosicky remains a part of his plans and is confident a new contract will be announced in the near future.
"Tomas Rosicky will stay. We have an agreement with him and it will come out soon," said the Frenchman
"I am absolutely adamant he has to stay at the club."
Wenger was impressed with Rosicky's role in the comprehensive victory which eased the anguish caused by the midweek Champions League defeat to Bayern Munich.
"He is maybe one of the players who plays the game of give and move, is a great accelerator of the game," said Wenger.
"When the ball comes to him it is 'boof'. It is second gear now and that is something I admire in him.
"He makes always things happen, not with individual dribbling but with individual acceleration of his passing and of his runs."
Ozil has received criticism for his recent Arsenal displays, particularly after his woeful penalty miss against Munich.
The German international sat out the visit of Sunderland with a minor injury, but team-mate Jack Wilshere believes he will soon regain his best form.
"Mesut is fine, he is a great character. He is friends with everyone around the place," the 22-year-old said.
"He has got a dead leg which is not nice, but he was in the dressing room helping the boys, talking to everyone, telling me and the other boys where to go (in midfield).
"He is a great talent and is up there with the best in the world and he will be all right."