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Integrated assessment models (IAMs) are a central tool for the quantitative analysis of climate change mitigation strategies. However, due to their global, cross-sectoral and centennial scope, IAMs cannot explicitly represent the spatio-temporal detail required to properly analyze the key role of variable renewable electricity (VRE) for decarbonizing the power sector and end-use electrification. In contrast, power sector models (PSMs) incorporate high spatio-temporal resolutions, but tend to have narrower scopes and shorter time horizons. To overcome these limitations, we present a novel methodology: an iterative and fully automated soft-coupling framework that combines the strengths of a IAM and a PSM. This framework uses the market values of power generation as well as the capture prices of demand in the PSM as price signals that change the capacity and power mix of the IAM. Hence, both models make endogenous investment decisions, leading to a joint solution. We apply the method to Germany in a proof-of-concept study using the IAM REMIND and the PSM DIETER, and confirm the theoretical prediction of almost-full convergence both in terms of decision variables and (shadow) prices. At the end of the iterative process, the absolute model difference between the generation shares of any generator type for any year is <5% for a simple configuration (no storage, no flexible demand), and 6-7% for a more realistic and detailed configuration (with storage and flexible demand). For the simple configuration, we mathematically show that this coupling scheme corresponds uniquely to an iterative mapping of the Lagrangians of two power sector optimization problems of different time resolutions, which can lead to a comprehensive model convergence of both decision variables and (shadow) prices. Since our approach is based on fundamental economic principles, it is applicable also to other IAM-PSM pairs.