The 30-year-old Senegal international was a free agent after leaving the Potters at the end of last season, with a fresh deal having taken several months to be agreed.
Chief executive Tony Scholes told the club's official website: "I am absolutely delighted we have managed to agree a deal to sign Salif.
"As supporters know, he has been Tony Pulis' top target for some months. He was an integral part of our squad last season and we are delighted to have him back." Manager Pulis added: "Salif is a fantastic player and I am obviously very, very happy to have him back.
"He is the sort of player that this football club needs to push on and we have shown our ambition by bringing him back here."