"I'm ecstatic to be back and I have worked hard to get there. Arsene Wenger is not stupid. He wouldn't have taken me back if he didn't like what he has seen."
Campbell played only one game for Notts County after leaving Portsmouth.
The former Tottenham defender joined the Magpies in August, with the involvement of former England manager Sven-Goran Eriksson a key factor in persuading him to drop down to League Two.
However, he left less than a month into a five-year deal and was strongly linked with a move to Championship leaders Newcastle.
He eased himself back into competitive football by playing for only the first half of the reserve match before being replaced by Ignasi Miquel, with there being no suggestion Campbell was injured.
Campbell, who was capped 73 times by England and played at two World Cups, was keen to resume his career as quickly as possible after settling his contract dispute with the Magpies.
It is understood offers were also on the table from Hull and Newcastle but Arsenal were always Campbell's first choice and he is still held in high regard by Wenger.
"He has a fantastic attitude and good fitness," said Wenger last week.
"Of course he is not the youngest but he is in a very good shape. He can still play in the Premier League, I've said that many times
"He is important in the dressing room as well. He's positive with the young players."
Campbell spent five years at Arsenal between 2001-2006, during which time he won two Premier League titles, three FA Cups and scored in the 2006 Champions League final defeat by Barcelona.
Wenger's decision to bring back the veteran defender, who will provide cover for Thomas Vermaelen and William Gallas along with 32-year-old Mikael Silvestre, will cast further doubt over the future of Philippe Senderos, who told BBC Sport he is keen to leave the club in pursuit of first team football.
Earlier this week, Arsenal great Bob Wilson said Campbell's return to the club would be a welcome one.
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