Nuddy was a free player and could talk and move to any club he so wished, but he and Neil Warnock agreed that talks between the player and the club would take place once he lands back in UK after Qualifying for African Cup of Nations.
Twelve months ago, the right-winger was forced on to the transfer market but this was to give the former Coventry City and Birmingham City star a warning and to fight for a first team place.
Neil Warnock told www.sufc.co.uk: "I'm absolutely delighted Peter has re-signed.
"He was inundated with offers but has taken a considerable cut in wages because he was desperate to continue playing for this club and the fans who have taken him to their hearts in the last year or so."