Michael Adebolajo, 29, was sentenced at the Old Bailey, London, in February.
The other killer was Michael Adebowale, 22, who was jailed for life with a minimum term of 45 years.
The pair were sentenced by Mr Justice Sweeney for butchering the 25-year-old father of one in daylight near Woolwich Barracks, London, last May 22.
Adebolajo's whole-life term condemns him to die behind bars.
Explaining his decision to give him a whole-life term, the judge said Adebolajo was the leader of the murderous plot and had "no real prospect of rehabilitation".
In January Adebolajo also filed for an application to appeal against his conviction.
Details about the grounds for the appeals have not been made public.