The two men were walking home from mosques in two British cities.
Police said on Tuesday they found no evidence that M. Abbkr, 27, was motivated by a particular ideology and the attack had not been treated as a terrorist attack.
Police said Abbkr poured petrol on both men before setting them alight using a lighter.
The two elderly men were set on fire in separate incidents as they walked home from mosques in west London in February and Birmingham, central England, in March.
"These were absolutely horrific attacks which almost defy belief in their apparent randomness and severity," West Midlands Police Chief Inspector Haroon Chughtai said.
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Abbkr, who had denied the offences on the basis of insanity, will be sentenced on Nov. 17.
One of the attacks left a man in his 80s in London suffering burns to his face and left hand.
The second man in Birmingham, who was in his 70s, was left with serious burns to his face and neck, and in need of skin grafts to his hands and face, police said.
Source: Reuters