The nineteen-year-old defender has moved to London Road on an initial one month loan deal after impressing Posh boss Barry Fry during the recent friendly game between the two sides.
"Elliott is a big strong defender and this loan deal gives us a chance to take a close look at him and we will see how it goes from there," Fry told the Posh official website.
"He is highly rated at West Ham, but he needs a few games under his belt because he missed a lot of last season."