Retired colonel William Endley, 55, had been providing advice to former-vice-president-turned-rebel-leader Riek Machar, whose forces have been fighting a civil war since 2013.
Children have been recruited by all sides of the conflict and have been forced to kill civilians, the commission found.
South Sudan's special high court has sentenced a South African military veteran to execution by hanging.
Endley's lawyer Gardit Abel Gar said they would launch an appeal.
The defense tried to get six witnesses to testify during the trial, but none went before the court.
Describing South Sudan's justice system as "dysfunctional" the commission called on the AU to establish the "Hybrid Court", modelled on tribunals in Sierra Leone, Cambodia and elsewhere.
Endley has been detained since August 2016.
"Our embassy in South Sudan will brief Head Office on the judgement and we will take it from there", said spokesman Nelson Kgwete.
On the whole, Ghanaian peacekeepers and police serving with UNMISS have made an excellent contribution to the protection of civilians and building of durable peace in South Sudan.
He was charged alongside James Dak, a former spokesman for Machar, who was also handed the death sentence for incitement and conspiracy against Kiir's government.
South Sudan gained independence from Sudan in 2011 and descended into civil war two years later, after Kiir sacked Machar as his deputy. More than 2 million people have fled the country, the largest refugee crisis since the Rwandan genocide 24 years ago.
The ceasefire agreement was meant to revive a 2015 peace deal, which lasted less than a year before collapsing. Millions who remain at home face hunger.
The UN said in a report on Friday that there is "sufficient evidence" both the government and rebels have committed war crimes.
Incidentally, Machar is now exiled in South Africa even though forces loyal to him continue to engage government forces in armed combat.
Cases included the deaths of two journalists, 58 arbitrary arrests or detentions of journalists or rights activists, 16 people fired from their jobs, the closure or suspension of three media houses, and censorship of newspaper articles and websites.