Prosecutors say Daniel Ignacio was convicted Tuesday of five counts of second degree murder, one count of fourth degree arson and other charges in the January 2010 blaze.
The 31-year-old faces 25 years to life in prison. He will be sentenced in Brooklyn Supreme Court on April 4.
Authorities say Ignacio used a cigarette lighter to ignite a roll of toilet paper which he then tossed on a baby carriage in the vestibule of the Bensonhurst building.
Prosecutors have also charged the building owners in the fire.