The trio, who were all sixteen at the time of the killing last October, have been sentenced to one years' youth detention rather than the three years recommended by the district court. The boys were found guilty of serious assault and manslaughter.
A fourth boy was cleared of all charges by both the district and appeals court.
A fifth boy, convicted incitement to commit assault by the lower court, has been cleared by the Court of Appeal. The court said prosecutors had been unable to prove that he was involved in the assault that led to Campogiani's death outside a Kungsholmen party venue.
The appeal court said its ruling was in line with standard sentencing for youth offenders.
"If they had been adults the punishment would have been six years in jail," the court wrote in its judgment.
The violent circumstances of Campogiani's death led to nationwide protests against street violence in the weeks following the killing.
The assault took place on the night of 5th October, when Campogiani came to blows with another boy. Prosecutors said that Campogiani was hit by the other boy, after which he retaliated.
Campogiani then ran away from the scene, but he was followed by a group of youths. At Kungsholmens Hamnplan he was hit again and fell to the ground. A number of the teenagers who had followed him kicked Campogiani on his head and upper body as he lay on the ground.
Campogiani's heart had stopped beating by the time the ambulance arrived. Doctors managed to restart his heart after he arrived at hospital, but later diagnosed massive brain haemmoraging. The teenager died less than two days after being admitted to hospital.
A week after the attack, 10,000 people gathered in Stockholm's Kungsträdgården to demonstrate against street violence. Smaller demonstrations were held elsewhere in Sweden.