Faye, 31, has also had spells with Newcastle, Rangers and Portsmouth, as well as French side Auxerre.
Wilkinson helped the Potters to promotion to the top flight last season and has made 12 appearances in all competitions so far this campaign.
Stoke chief executive Tony Scholes told the club's website: "Although at this time the attention is on players that we may be bringing in, the players who are at the football club are the most important ones.
"We're delighted to have both Amdy and Andy commit their medium-term futures to the club and sign extensions to their deals."
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