Campbell, 35, who had been training with Arsenal after a short spell with League Two Notts County ended abruptly in September after one game, played in the Gunners 4-2 reserve win over West Ham at Upton Park on Tuesday.
"I'm ecstatic really to be back at Arsenal, and I have worked bloody hard to get there," Campbell told The Independent after the match.
"I hope to sign for Arsenal until the end of the season. There are still a few technicalities to iron out, but it's fantastic, great, marvellous. The old enthusiasm is back. I've got to tell you it seems as though I have never been away."
"Arsene has been an inspiration," Campbell said.
"He has watched me closely after letting me train at Arsenal for nearly two months now.
"He's not stupid, he wouldn't have taken me back if he didn't like what he had seen, and I have worked and worked. I do believe I can contribute. I really have my confidence and fitness back and believe I can make a big, big contribution."
Campbell is likely to be reserve for Arsenal's first choice central defenders William Gallas and Thomas Vermaelen but his arrival is likely to see Swiss defender Phillipe Senderos, who is keen for first-team football ahead of the World Cup, depart.
The moved would complete a remarkable turnaround for Campbell whose career looked over after his departure from Notts County but he could soon look forward to being part of third place Arsenal's Premier League and Champions League title challenges.
However, Campbell's time at Arsenal ended disappointingly through injuries and a loss of form.
