The 48-year-old former England international striker joined the Hammers on a part-time basis on Friday.
Allardyce now hopes that Sheringham can help his forwards score more freely when they return to action next season.
"Teddy was interested in coming into coaching at this stage so we're obviously glad to have him on board to give us a new outlook on how we are working with our attacking players," Allardyce told the club's official website.
"We hope he can give some individual expertise and one-on-one coaching with our attacking lads to hopefully help us to score a few more goals.
"Everybody knows how long he played, into his forties, and he spent the latter part of his career at West Ham so he knows all about the club and we're all looking forward to him joining us and being part of our very highly-qualified staff."
Sheringham played for West Ham between 2004 and 2007.