Ntaganda surrendered Monday at the U.S. Embassy in Kigali. The Rwandan-born warlord, an ethnic Tutsi, served as the leader of the rebel March 23 movement, which is accused of war crimes during fighting in the Democratic Republic of Congo.
M23 allegedly has the support of the Rwanda government, an allegation Kigali denies.
Rights groups ranging from Global Witness to Human Rights Watch hailed Ntaganda's surrender, calling on the U.S. government to facilitate his safe transfer to The Hague.
"Surrendering Bosco Ntaganda to the ICC should act as a strong deterrent to others and help break persistent cycles of impunity that wrack eastern DRC," Amnesty International's Deputy Africa Director Sarah Jackson said.
U.S. State Department spokeswoman Victoria Nuland confirmed Ntaganda's surrender in a statement Monday. The United States and Rwanda aren't party to the Rome Statue that created the ICC.
British Foreign Secretary William Hague said Tuesday his government supported the rebel leader's transfer to the ICC.
"I urge all to cooperate in facilitating this transfer as quickly as possible," he said in a statement.
DRC Ambassador to the United Kingdom Kikaya bin Karubi told the BBC it's time for Ntaganda to "face the music."
Ntaganda claims he's innocent.