Amanda Hutton, 43, showed no emotion as she was convicted of manslaughter by a jury at Bradford Crown Court.
The court heard Hamzah's mummified body was found in Hutton's Bradford bedroom almost two years after he died in December 2009.
Jurors returned their verdict to a packed court after almost five hours of deliberations. The foreman of the jury made clear they had convicted her on the basis she was grossly negligent by not providing adequate nourishment for Hamzah.
Hutton was remanded in custody and will be sentenced today by Judge Roger Thomas QC.
Speaking outside court, Malcolm Taylor, from the Crown Prosecution Service, said: "This was a truly tragic case involving the death of a little boy, Hamzah Khan, whose body, showing signs of extreme malnutrition, was discovered amid scenes of the most appalling squalor at the family home in Bradford."
Hutton, 43, had denied killing Hamzah, whose decomposed and insect-infested body was found in a travel cot in her bedroom. A two-week trial heard his remains had been in the cot for almost two years when they were found by police searching the house on September 21 2011.
The little boy had died on December 15, 2009.
The jury heard Hamzah's body was found in the house in the Heaton area of the city in terrible squalor, where five other school-aged siblings were living.
Hutton admitted a charge of child cruelty in respect of each of these children, aged between five and 13 in 2011.
Prosecutors told the jury of eight men and four women Hamzah probably died from malnutrition because Hutton neglected him as she concentrated on her alcohol addiction.
But Hutton told the court her son died suddenly and she only kept claiming his child benefit because she was worried that if she stopped his body would be discovered.