The 32-year-old Sodje, who comes back to England after a stint in China, has scored three goals in summer friendlies for North End and will now make his move to Deepdale official subject to international clearance.
Westley told Preston's official website: "Akpo has been at the club during pre-season and he has made a positive impact on me.
"We have agreed a short-term deal, he has been training well and he has played well when he has been involved in games and the opportunity to have a further look at him is one I am delighted to have."
Sodje added: "It is really good to complete the move. I have been at the club for almost three weeks and now I can concentrate on playing for Preston North End.
"It doesn't feel like I am settling into a new place but that is down to the rest of the boys and the club, they all made me feel welcomed on my first day."
