The tribunal found Milosevic, no relation to Slobodan Milosevic, the former Yugoslav president, guilty of terror and on one count of war crimes, as well as murder, inhumane acts and crimes against humanity.
Human-rights organisations estimate that nearly 12,000 people, including 1,500 children, died during the blockade of the city.
In one attack, 43 people were killed and 75 wounded when a mortar shell hit people queuing for bread by the city market in August 1995.
Judge Robinson said it was under Milosevic's command that modified air bombs, known to be inaccurate weapons, were first used and he decided on the placement of bomb launchers.
"Each time a modified air bomb was launched the accused was playing with the lives of the citizens of Sarajevo," he said.
Milosevic commanded 18,000 Bosnian Serb troops during the siege of Sarajevo, taking over command from Stanislav Galic, another former Bosnian Serb general already sentenced to life imprisonment for his role in the siege, in August 1994.
The International Criminal Tribunal for the former Yugoslavia convicted him of five charges, including leading a campaign of terror, murder and inhumane acts.
Milosevic had denied all charges, arguing that the Bosnian capital was a battle ground during the siege and his troops were carrying out legitimate military operations.