The Arsenal striker has swapped the Emirates Stadium for Upton Park and Allardyce is hopeful that the forward can rediscover the form which fired Bordeaux to the Ligue 1 title in 2009.
Allardyce told reporters: "He's itching and hungry to get back and show what he can do. We'll try and get him to be that goal threat that he was at Bordeaux.
"Obviously he's been very disappointed with his lack of involvement at Arsenal.
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"Now with Olivier Giroud, they will cross balls for him. Obviously it hasn't worked there but hopefully it will work for us.
"We'll give him the platform by feeding him the right type of balls. You provide the service he needs in terms of how he plays. He's exceptionally good in the air and he's really good at getting between defenders from crosses. We can provide the ammunition for him to hopefully get a few goals."
The Hammers' boss now has a tough choice to make up front, with Chamakh joining Carlton Cole and Andy Carroll in the fight for just one spot in attack, but the 58-year-old believes added competition will be a boost to each of them.
"For all three of them there's a challenge for places," said Allardyce.
"Play your best and keep the shirt. If you don't play your best you lose the shirt. All three of them will get the chance to play and whoever plays the best will stay in for me."