Michael Adebolajo, who was found guilty of the murder of British soldier Lee Rigby, has lodged an application to appeal against his conviction, the Judicial Office has confirmed.
Fusilier Rigby was killed on 22 May 2013 in Woolwich, south-east London.
Adebolajo, 29, from Romford, east London, said he was a "soldier of Allah" and it was an act of war.
He and Michael Adebowale, 22, from Greenwich, south-east London, are currently awaiting sentencing.
Mr Justice Sweeney said he would pass sentence on the two men after a key Appeal Court ruling on the use of whole-life terms, with the decision due at a later date.
In December, an Old Bailey jury of eight women and four men took approximately 90 minutes to find the men guilty of murdering Fusilier Rigby.
They were found not guilty of attempting to murder a police officer at the scene.
The jury had heard that Adebolajo and Adebowale drove a car into Fusilier Rigby at 30-40mph, before dragging him into the road, attacking him with knives and attempting to decapitate him with a meat cleaver.
In court, Adebolajo - a married father-of-six - admitted killing Fusilier Rigby, 25, but denied murder and described the killing as a "military operation".
As the guilty verdict was declared and the defendants were taken out of the courtroom, Adebolajo kissed his Koran and raised it in the air.
In a previous police interview, Adebolajo had said he and Adebowale decided to lie in wait near Woolwich barracks and targeted Fusilier Rigby because he was wearing a Help for Heroes hooded top and carrying a camouflage rucksack.
As a police vehicle approached, the men rushed towards it, waving the meat cleaver and a firearm.
They were both shot, but denied attempting to kill police, saying they had wanted armed officers to shoot them dead so they could "achieve martyrdom".
An investigation by the Independent Police Complaints Commission (IPCC) later concluded the police officers who shot the men "acted appropriately to the immediate threat".
The Judicial Office, which reports to the Lord Chief Justice and supports the judiciary in its work upholding the rule of law, confirmed on Thursday that Adebolajo wished to appeal against his conviction.