Only paperwork stands in the way of the deal being completed and manager is looking forward to seeing the striker combine with top-scorer Robin van Persie once again
The French forward has been training with his former club during the MLS offseason and now looks set to contribute to the first team.
"For two months it certainly will happen. I don't take care of the agreement and the insurance and that is not completed," Wenger told reporters.
The Red Bulls have shown no indication of wanting to block the two-month move but are understood to be waiting for a final agreement on the insurance policy before definitively allowing the deal to go through.
"At the moment we cannot announce anything because all the paperwork is not done," Wenger said.If Henry does return he will be available for Premier League games against Manchester United and Tottenham as well as Arsenal's Champions League clash with AC Milan.
"To cover for two months is ideal," Wenger added. "He has the experience and the quality. He knows the club and can help the players on and off the pitch. He has exceptional talent and is a very intelligent man, it can only be positive."
Wenger believes Henry still has enough quality to make an impact in the Premier League and is excited about the prospect of him and captain Robin van Persie playing together.
"He is still class and has quality. He still has pace," Wenger said. "When Robin and Thierry play together we will do very well."
Arsenal has brought former players back to the club in times of emergency in recent years with Sol Campbell and Jens Lehmann re-signing to play and Wenger suggested this trend may continue.
"It shows that Arsenal is always special to players, such as Sol Campbell, Jens Lehmann and now Thierry," he said. "We are not looking for permanent players unless we lose players, as we have a big squad."
Wenger also confirmed that the deal was not pressured by Henry and that he was fully behind it, saying, "It was my idea. He was happy about it, but it was my idea.
"No one expects him to be what he was 10 years ago. There's no special pressure, Robin remains our main striker."
Reports on Friday suggested Henry will wear the No.12 shirt in his second spell at the club due to the fact his old No.14 shirt is taken by Theo Walcott.
Henry is Arsenal's all-time leading scorer, having netted 226 times in eight years after joining from Juventus in 1999. He is still idolized by the fans and the club recently unveiled a statue of him outside the Emirates Stadium.