The Senegal international became the Potters' third buy in the January transfer window after securing a work permit.
Ndiaye, presented at the bet365 Stadium during the half time of Stoke's league tie against Watford, is 'very happy' to join Paul Lambert's side.
“I am very happy to join Stoke City, a very big club in England - it is a proud moment for me,” Ndiaye told club website.
“There have been many talks this month but I wanted to join Stoke City, so to be here now is very exciting for me and I am looking forward to helping the team move forward.
“I knew many good things about the Club, I spoke to friends who play in the Premier League and I also spoke to Mame Diouf, who is a very good friend of mine.
“They were all very positive and made me very excited to make this move, so as I have said before I am just very happy to be here now.”
“The Premier League is a league that everybody wants to play in, so I am proud to be here, but I know that I have to continue to improve and do everything I can to help Stoke City.”