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Background: Dengue dynamics are driven by complex interactions between human-hosts, mosquito-vectors and viruses that are influenced by environmental and climatic factors. The objectives of this study were to analyze and model the relationships between climate, Aedes aegypti vectors and dengue outbreaks in Noumea (New Caledonia), and to provide an early warning system. Methodology/Principal Findings: Epidemiological and meteorological data were analyzed from 1971 to 2010 in Noumea. Entomological surveillance indices were available from March 2000 to December 2009. During epidemic years, the distribution of dengue cases was highly seasonal. The epidemic peak (March–April) lagged the warmest temperature by 1–2 months and was in phase with maximum precipitations, relative humidity and entomological indices. Significant inter-annual correlations were observed between the risk of outbreak and summertime temperature, precipitations or relative humidity but not ENSO. Climate-based multivariate non-linear models were developed to estimate the yearly risk of dengue outbreak in Noumea. The best explicative meteorological variables were the number of days with maximal temperature exceeding 32°C during January–February–March and the number of days with maximal relative humidity exceeding 95% during January. The best predictive variables were the maximal temperature in December and maximal relative humidity during October–November–December of the previous year. For a probability of dengue outbreak above 65% in leave-one-out cross validation, the explicative model predicted 94% of the epidemic years and 79% of the non epidemic years, and the predictive model 79% and 65%, respectively. Conclusions/Significance: The epidemic dynamics of dengue in Noumea were essentially driven by climate during the last forty years. Specific conditions based on maximal temperature and relative humidity thresholds were determinant in outbreaks occurrence. Their persistence was also crucial. An operational model that will enable health authorities to anticipate the outbreak risk was successfully developed. Similar models may be developed to improve dengue management in other countries. Author Summary: Dengue fever is a major public health problem in the tropics and subtropics. Since no vaccine exists, understanding and predicting outbreaks remain of crucial interest. Climate influences the mosquito-vector biology and the viral transmission cycle. Its impact on dengue dynamics is of growing interest. We analyzed the epidemiology of dengue in Noumea (New Caledonia) from 1971 to 2010 and its relationships with local and remote climate conditions using an original approach combining a comparison of epidemic and non epidemic years, bivariate and multivariate analyses. We found that the occurrence of outbreaks in Noumea was strongly influenced by climate during the last forty years. Efficient models were developed to estimate the yearly risk of outbreak as a function of two meteorological variables that were contemporaneous (explicative model) or prior (predictive model) to the outbreak onset. Local threshold values of maximal temperature and relative humidity were identified. Our results provide new insights to understand the link between climate and dengue outbreaks, and have a substantial impact on dengue management in New Caledonia since the health authorities have integrated these models into their decision making process and vector control policies. This raises the possibility to provide similar early warning systems in other countries. [ABSTRACT FROM AUTHOR]