"The deal has taken a long time to come through but he's a good addition who can play at right-back and centre-half," Vale boss Martin Foyle told the club's official website.
"Rhys is a leader and a talker which is something we haven't had and what we need.
"Because he played at Cardiff we had to go through the Welsh FA and the Norwegian FA which was a bit of a nightmare but he'll be involved at Chesterfield next Saturday."
Weston has signed a short term deal that lasts until the end of this season.