The Niger Delta region of Nigeria is the bedrock of the Nigerian economy making the country the sixth oil producing nation in the world. The communities in this region are faced with adverse effects of the ever changing climate and environmental degradation resulting from exploitation and exploration activities of the multinational oil companies. The study highlights in details the climatic and environmental changes that have occurred in the Niger Delta region and shows the relationship between these changes and poverty. The study elaborates on the inherent adaptive strategies that has been adopted by the people of the Niger Delta and suggest ways to strengthen existing capacity of the people to adapt to climate change and adverse environmental changes. It reveals the weaknesses and deficiencies in the Nigerian Constitution in administering environmental rights to the people and suggests institutional and constitutional solution to solving these problems in the region.