Allardyce has spoken to Moyes since the Scottish boss took the job at the London Stadium.
And the former Hammers boss has full faith that Moyes will be able to turn around West Ham’s fortunes, during his time at the helm.
"He will do, I guarantee that, because having spoken to him he’s so determined to show how good a manager he is," Allardyce said.
"He has his own drive and determination, as well as wanting to get West Ham up the table. He needs to use his experience now to get the best out of that squad."
Moyes’ appointment has not been greeted well by many West Ham supporters, who feel it shows a lack of ambition.
Moyes has failed in his last three jobs - at Manchester United, Real Sociedad and Sunderland - and there are doubts over whether he will be the right man to help West Ham move up the table.
The Hammers are currently in 18th place in the top flight standings, after what has been a terrible campaign so far.
Moyes will take charge of West Ham for the first time after the international break, when the Hammers take on Watford at Vicarage Road.