The former colonies of Germany and the Ottoman Empire were transferred to the League of Nations, which then extended conditional control of those areas to colonial powers under a League of Nations mandate. Britain and France occupied most of these colonies because 1) they could argue they had experience governing in these regions and 2) they had already militarily occupied those colonies.

In the Pacific, much of Germany's empire came under the South Pacific Mandate of Japan. Australia and New Zealand governed several mandates jointly with Britain. And German Southwest Africa (the future Namibia) was governed by South Africa.

Oh, and I forgot one: Rwanda and Burundi were split from German East Africa and attached to the Belgian Congo.