The Asia-Pacific region has gradually become a driver of global economic growth, with economic integration agreements (EIAs) and climate distance playing increasingly important roles in the agri-food trade in the 21st century. The recent signing and implementation of the Regional Comprehensive Economic Partnership (RCEP) and the Comprehensive and Progressive Agreement for Trans-Pacific Partnership (CPTPP) have garnered global attention. This study examines the roles of different types of regional trade agreements and climate distance in the agri-food trade in the Asia-Pacific region and constructs a trade system involving 19 member countries of the RCEP and the CPTPP by analyzing panel data from 2003 to 2022. The Poisson pseudo-maximum likelihood estimator is employed to estimate an augmented gravity model that considers domestic trade flows, endogeneity issues, reverse causality, globalization effects, long-term effects, and overlapping membership. The empirical findings demonstrate that partial scope agreements and EIAs significantly promote bilateral agri-food trade, whereas temperature distance acts as a barrier and precipitation distance has a negligible effect. Overlapping members of the RCEP and CPTPP exhibit cumulative positive effects three years after the implementation of EIAs, resulting in an approximately 52.1% increase in the bilateral agri-food trade after ten years. Additionally, overlapping membership mitigates the long-term negative impact of temperature distance. This study reveals that the seven overlapping members of the RCEP and CPTPP in the Asia-Pacific region achieve greater benefits more quickly through EIAs, suggesting that overlapping membership can be an effective adaptive strategy for dealing with climate change.