The 47-year-old will stand in for the late star on the BBC One tribute show, which will be titled Jim'll Fix It with Shane Richie.
Jimmy's series, which ran between 1975 and 1994, saw the wishes of young viewers being granted.
According to British newspaper The Sun, EastEnders actor Richie said: 'It was compulsive television in our house and all my friends would talk about the 'fix its'.
'I even wrote in but wasn't one of the lucky ones! I'm honoured to be part of this Christmas Special and salute Sir Jimmy and fix it for a new generation.'
Savile was buried in a gold coffin in Scarborough, North Yorkshire, last week.