The 35-year old played for the Latics for three years before moving to Fratton Park in 2002.
Pompey's Peter Storrie said: "It's disappointing the way it has turned out and we want Arjan to stay and compete for his place.
"We have reluctantly agreed terms with Wigan and to be honest we feel our hands are tied over this after the player put in his transfer request. However nothing has been concluded."
Storrie told the club's wesbite: "Nobody knows what would have happen if he stayed and it is quite possible he could impress the manager and become a main feature all season, which is what it is all about in any level of football."
Latics boss Paul Jewell has worked with de Zeeuw before in his last spell with Wigan and has described the defender as a "leader".
Jewell said: "Without doubt, he is the best professional I have ever worked with. There have been some good ones but he is the ultimate.
"I was very disappointed to lose him in the first place and while, yes, he is 35, he also retains a great desire. His fitness levels are high and he is a leader."
Since winning promtion to the Premiership, Jewell has been busy in the transfer market with six player including Liverpool's Stephane Henchoz now added to his squad, while he also tried to sign Scott Parker from Chelsea.
Wolves striker Henri Camara is expected to sign for Jewell before the start of Wigan's campaign against defending champions Chelsea on Sunday.