Danai Muhammadi, 24, a used car salesman who was born in Iran, was found guilty of three counts of murder and two of attempted murder, The Sun reported. His mother-in-law, Amanda Crook, and his brother-in-law escaped the burning home in Chatham, Kent.
Farhad Mahmud, a nightclub bouncer from Maidstone, Kent, was also convicted of murder and attempted murder. Muhammadi's girlfriend, Emma Smith, 21, of Coventry, was found guilty of manslaughter for urging him to kill his wife.
Sentencing was set for July in Crown Court in Maidstone.
Muhammadi's wife, Melissa, 20, who had left him and returned to her parents' home, died in the fire in September 2011, holding her son, Noah, 15 months. Her father, Mark Crook, was also killed.
The blaze was set by pumping gasoline through the mail slot and setting it on fire. Muhammadi was caught by a security camera filling a garden sprayer with gasoline shortly before the fire.