Their convictions in July last year were the first handed down by Sierra Leone's war crimes tribunal.
'Brutal and atrocious crimes'
The convictions were the first by any international court on the conscription of child soldiers - who were often drugged and forced into battle during the West African country's 1991-2002 war.
George Gelaga-King, the presiding Judge Justice, said the appeals panel "took into consideration the gravity of the crimes committed, as being the most heinous, brutal and atrocious crimes ever recorded in human history".
The three men - Alex Tamba Brima, Santigie Borbor Kanu and Brima Bazzy Kamara - went on trial in Freetown, Sierra Leone's capital, in 2005, two years after their indictment.
They were convicted of 11 war crimes charges, including terrorism, enslavement, rape and murder.
Because of security concerns, the three were expected to serve their prison time outside of Sierra Leone - most likely in Europe, though it has yet to be decided where.
"A few countries have offered to take them in," a court spokesman told reporters after the ruling.
He did not name the countries, but last year both Austria and Sweden had volunteered to take them as inmates and pay their expenses.
The special tribunal was set up following the Sierra Leone's 10-year conflict, in which about a half-million people died and rebels engaged in rape, pillaging and cutting off the limbs of thousands of civilians.