It is widely acknowledged that there exists a strong and intricate connection between climate change and the building sector, which is evident in the reciprocal environmental impacts. To mitigate climate change, the circular economy has been introduced as a potential strategy. Nevertheless, the building sector faces significant challenges in fully and effectively incorporating the circular economy. These challenges arise from this sector’s conservative and complex nature, which lacks flexibility hindering the full and effective transition toward the circular economy. This paper examines the research question of how to implement the circular economy effectively in the building sector for climate change mitigation. To answer the research question, this paper states that the environmental impacts associated with the building life cycle phases are related to each other, and their cause is embedded in the selected design choices and solutions in the design phase. Therefore, this paper, focusing on the abovementioned issue, specifically on the crucial design phase, employed a methodological approach which is called a stakeholder-centric approach based on a systematic critical literature review methodology. This paper, consequently, identifies the stakeholders, clarifies their roles and objectives in the design phase, and investigates the connection between stakeholders’ roles and the environmental impacts due to their actions. The results uncover the actionable counteractions and potential solutions tailored to each stakeholder, emphasizing the necessity of a collaborative, well-informed, and environmentally conscious approach that stakeholders could undertake to effectively contribute to the reduction of environmental impacts and the mitigation of climate change. This paper concludes that to implement the circular economy in the building sector effectively, all the stakeholders involved must adopt a transformative mindset that prioritizes sustainable practices, innovation, and environmental responsibility. With the presence of the limitations, the novelty of this paper lies in its emphasis on the stakeholder concept at the design phase concerning the aforementioned relationship.