Mrs Turei will be responsible for housing, and fourth-ranked list MP Eugenie Sage will take over primary industries job from 14th-ranked MP Steffan Browning.
Explaining the change, Mr Shaw said: "The primary industries are a core part of the New Zealand economy, and provide some of the most exciting opportunities to transition our economy into a smarter, cleaner future."
Julie Anne Genter will take over the finance portfolio, which was previously held by Dr Norman.
MP | Portfolio
Metiria Turei: Inequality, Building and Housing (inc. Social Housing, HNZ), Maori Affairs
James Shaw: Climate Change, Economic Development
Russel Norman: Trade, Justice (electoral), National Intelligence and Security (inc. NZSIS, GCSB)
Kevin Hague: Health (inc. ACC, Sport & Recreation), Conservation, Rainbow Issues
Eugenie Sage: Environment, Primary Industries, Land Information, Canterbury Earthquake Recovery, Earthquake Commission
Gareth Hughes: Energy and Resources, Tertiary Education, Skills and Employment, Science and Innovation, ICT, Broadcasting, Wellington Issues
Catherine Delahunty: Education (inc. Novopay), Water, Human Rights, Te Tiriti o Waitangi
Kennedy Graham:, Foreign Affairs (inc. Defence, Disarmament, Customs), Veterans Affairs, Senior Citizens
Julie Genter: Finance (inc. Revenue, SOEs), Transport, Youth
Mojo Mathers: Commerce and Consumer Affairs (inc. Regulatory Reform), Disability Issues, Animal Welfare
Jan Logie: Social Development (inc. Women, Community and Voluntary Sector), State Services, Local Government (inc. Civil Defence), Rainbow Issues
Dave Clendon: Tourism, Small Business, Criminal Justice (inc. Courts, Corrections, Police), Musterer
Denise Roche: Workplace Relations and Safety, Waste, Immigration, Pacific Peoples, Ethnic Affairs, Internal Affairs (inc. Statistics, Arts Culture and Heritage, Ministerial Services, Racing, Gambling), Auckland Issues
Steffan Browning: Organics, GE, Biosecurity, Pesticides, Food Safety