England will have to face Australia in the Glasgow Games while Wales will face South Pacific nations Samoa and Papua New Guinea, as well as Malaysia, in their group.
The All Blacks have won all four Commonwealth gold medals so far and will also take on Nigeria and Canada in their group.
England face Sri Lanka and Uganda in their pool games.
Sixteen teams take part in the tournament, including South Africa, which will be held at Ibrox Stadium on July 26-27.
COMMENT RULES: Comments that are judged to be defamatory, abusive or in bad taste are not acceptable and contributors who consistently fall below certain criteria will be permanently blacklisted. The moderator will not enter into debate with individual contributors and the moderator’s decision is final. It is Belfast Telegraph policy to close comments on court cases, tribunals and active legal investigations. We may also close comments on articles which are being targeted for abuse. Problems with commenting? email@example.com