Sullivan has earlier this week predicted the Hammers were set to land the experienced young international.
“I am absolutely delighted to have clinched the signing of Cheikhou after weeks of tough negotiations that saw us beat off the challenge of some huge clubs across Europe for his signature,” Sullivan said.
“He comes with vast experience at the top level - including the Champions League - despite being only 24 and I am sure he will add valuable competition to places.
“We are determined to have a better season this year and this signing is a statement of the direction the Club is heading in. We hope to have at least four more signings in place by the time we kick-off against Tottenham on 16 August as we aim for at least a top-ten finish this season.”