Shaun Pinner, 48, has formally lodged papers in the Donetsk People’s Republic (DPR), the Russian-backed separatist region, said TASS on Friday. Another Briton also sentenced to death, Aiden Aslin, had not yet submitted an appeal, added the agency.
A third man condemned with the Britons, Brahim Saadoun from Morocco, had also lodged an appeal against his death sentence.
Mr Pinner, originally from Watford, is a former waste manager. He is said to have moved to Ukraine several years ago with his wife, and later joined the country’s armed forces.
He was also a member of a regular Ukrainian military unit and surrendered to pro-Russian forces in Mariupol in April.
His three-year military contract was due to end later this year and he was planning to enter a humanitarian role within Ukraine, according to reports quoting his lawyer.
He was accused of “conducting terrorist acts” and attacking military personnel as well as settlements and civilians.
Meanwhile, Mr Aslin, 28, who also goes by the name Johnny, is a former care worker from Newark, Nottinghamshire.
He had been fighting alongside regular Ukrainian military units in Mariupol and surrendered in the southern port city in mid-April.
Mr Aslin had spent time fighting against Isis in Syria with Kurdish forces before travelling to Ukraine.
Both Britons have been found guilty of taking action towards violent seizure of power at a court in the DPR earlier this month. The men were accused of being “mercenaries” after fighting with Ukrainian troops, a charge that carries the death penalty in the unrecognised territory.
Earlier this week, The European Court of Human Rights (ECHR) said it had issued interim measures to instruct Moscow to ensure a stay of execution for all three men being held captive.
The ECHR also requested that the Russian government provide information, in two weeks, to show what actions and measures have been taken by their authorities