The centre-back made the surprise decision to sign a five-year contract at Meadow Lane in the summer after his contract expired at Portsmouth.
But reports on Wednesday morning suggested Campbell had walked away from County, who have the 35-year-old's ex-England boss Sven Goran Eriksson as director of football.
That speculation has now been confirmed, with the 73-time England cap saying his goodbyes to his short-term team-mates after training on Tuesday.
Campbell struggled on his debut for County as Ian McParland's side lost to Morecambe on Saturday and it is understood he asked to be released from his deal after that match.