Around 100 U.S. troops ended a six-year mission earlier in 2017 after failing to capture Kony, whose group has co-opted tens of thousands of children into conflict.
The events at The Hague should send another strong message that such war crimes will no longer be tolerated.
The soldiers were based in Central African Republic and received assistance from U.S. special advisers in hunting the warlord.
Kony's group killed thousands of people and kidnapped tens of thousands of children, forcing them into combat.
Kony, the head of the Lord's Resistance Army, remains on the run.
Ongwen, a former Lord's Resistance Army commander, faces 70 charges at the ICC.
Kony's notorious militant group has kidnapped more than 200 people so far this year.
Kony's Lord's Resistance Army still has a few hundred fighters scattered across central Africa.