The Czech playmaker stood in for Mesut Ozil, who was carrying a thigh injury, against Sunderland and was instrumental in the Gunners' 4-1 victory at the Emirates Stadium, where he scored a well-executed third goal.
Rosicky joined Arsenal from Borussia Dortmund in 2006, but has seen his time in London hampered by a string of injuries.
The creative midfielder is out of contract in the summer and will turn 34 in October, but Wenger revealed a deal for an extension was close to being announced.
"Tomas Rosicky will stay. We have an agreement with him and it will come out soon," the Arsenal boss said.
"I am absolutely adamant he has to stay at the club."
Wenger was impressed with Rosicky's contribution to what was an accomplished display on the back of the disappointing 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," Wenger said.
"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."
Wenger added: "When he arrived here he was less a tactical player and more the 'Mozart from Prague' and he was purely creative, offensive player.
"Today he is a real organiser on the pitch as well. I like to have him in the team because he gives a real structure to our team."
Midfielder Jack Wilshere feels the Gunners just need to find the right focus to meet those challenges head on.
"When you are playing, you have to get into the right mental level as well," the England international said.
"Physically we are all in great condition, we train hard, but if you are not at the right mental level you are not going to be able to perform.
"It is about getting to that level before the game, getting yourself ready and then we can take it onto the pitch."
Much has been made of Ozil's inconsistencies since his club-record B£42.5million move from Real Madrid at the end of the summer transfer window, which were highlight by an early penalty miss against Bayern which would have put Arsenal ahead.
Wilshere, though, insists there is nothing to be concerned about.
"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."
- Sports & Recreation
- Mesut Ozil
- Borussia Dortmund