The 33-year-old defender, who has been released by Stoke, was rumoured to be a target for Celtic as well as a number of clubs on the continent.
But having played under Allardyce at Bolton and Newcastle, Faye was delighted to become the new Hammers manager's first signing since taking over at Upton Park.
"Sam is a very good manager and I am very pleased to be playing for him again," Faye told West Ham TV. "He gave me a chance here in England and he is someone who gives me confidence.
"I did well in Bolton and Newcastle and I have gone to clubs to help him and to help me, and I'm very proud he likes me. I'm very happy to work for him.
"He likes strong teams who work hard. He is a good manager - the best manager. He can get the best out of players. Everyone respects him because he is a good manager. He will do well at West Ham."