Faye will join the Hammers on a free transfer once his contract expires at Stoke at the end of the month.
Faye worked with Allardyce at Bolton in 2005 and again at Newcastle in 2007, before joining the Potters in 2008.
The Senegal international will bring a wealth of experience with him as the Hammers look to replace a number of their squad as they prepare to try and return to the Premier League at the first attempt.