The 35-year-old is the first player Wenger has re-signed and the veteran defender is determined to prove his worth to his old boss.
He told The Sun: “It’s a great compliment that I’m the first player Arsene’s re-signed.
“I’ve got to repay that faith. I have to contribute. It’s a long season, there are big games coming up. Hopefully it all goes well and I play some games.”
“The likes of me and William Gallas have seen it all before and that’s what it’s all about really,” he added.
“It’s showing the young lads when you’ve got that green light just keep it going.
“When the games are coming thick and fast and you need a win here or a draw and everyone’s tired, it’s just dragging the lads over the line and getting the result.”
He added: “If the club carry on training me like this, I can keep going for two or three years playing real good quality. It’s all about determination.
“Now, I can play and I’ve been given a chance and I’m desperate to play. I’m in better shape than I was in the summer, big-time. All the Arsenal staff have done wonders.
“My dream is to stay on past the end of the season but who knows? People like Franco Baresi and Paolo Maldini are an inspiration. The main thing is whenever I get a chance I want to bloody show what I can do.
“David James playing for England at 40 is an inspiration to me. But the main thing for me is step-by-step and go from there. It’s a dream, a dream come true to be back at Arsenal.
“I had other offers but some people mucked around. Arsene said ‘Right, this is it’ and I said ‘OK, let’s make it happen’.”