The versatile 29-year-old was a free agent after leaving Crawley at the end of last season.
Cooper scored twice in 14 appearances for Pompey last term after arriving on loan from the Red Devils in January.
"It's nice to be back concentrating on football after an extended summer," he told the club website.
"I'm pleased to get the deal done and to come back to a club that now has a different feel about the place.
"Everybody knows about the problems last season with so many players coming and going, but it's nice to come back for a new beginning.
"The pitch and the stadium look great and I'm looking forward to getting going once again."