Cobb County Juvenile Court Judge Gregory Poole last month found the boy not guilty of murder but convicted him of two counts of battery.
Poole sentenced him to probation and anger management classes on Wednesday. He could have spent the next two years in juvenile detention.
"The purpose of the juvenile court is to fix problems, not punish people," Poole said. "If he gets through this, he will be a success story."
The boy was visiting relatives in the Atlanta area in July. The baby's mother, Brittiany Young of Kennesaw, said she left the children alone in the car July 4 while she shopped and returned to find her baby, Millan Young, limp and unresponsive. The infant died a day later.
Prosecutors said the boy shook his cousin and slammed her head against a hard surface.
The boy has been in juvenile detention since July. He was ordered to live with a relative in the Atlanta area but will be allowed to visit his mother in Tampa.
"He needs to be with family, and he needs a lot of love," said his grandmother, Joyce Hightower.