Kenya, which has 100 suspects awaiting trial and has already convicted 18 pirates, had said it would stop prosecutions unless other countries agreed to share the "burden".
Pirates based in neighboring Somalia have made the Gulf of Aden one of the world's most dangerous shipping lanes.
The court is being funded to the tune of $5 million by several donors, including the United Nations Office on Drugs and Crime, the European Union, Australia and Canada.
Convicted pirates will serve their sentence in the same prison where they awaited trial and where they new courtroom is.
Confusion over legal proceedings against alleged pirates has resulted in some international patrols in the India Ocean releasing some suspects they had detained, the BBC reports.