Campbell left Arsenal in July looking "for a fresh challenge" and attracted interest from Turkey's Fenerbahce.
The decision to move to Portsmouth puzzled Arsenal manager Arsene Wenger.
Campbell, 31, made 197 appearances after joining the Gunners from crosstown rival Tottenham in 2001, the AP reports.
During Campbell's five years, Arsenal won five major trophies, including two league titles and three FA Cups. He has made 69 appearances for England and was a member of the national squad at the 1998, 2002 and 2006 World Cups.
First and foremost, it goes about the replacement of the French-Russian SaM146 engine with the Russian PD-8 aircraft engine