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We present a joint cosmic shear analysis of the Dark Energy Survey (DES Y3)and the Kilo-Degree Survey (KiDS-1000) in a collaborative effort between thetwo survey teams. We find consistent cosmological parameter constraints betweenDES Y3 and KiDS-1000 which, when combined in a joint-survey analysis, constrainthe parameter $S_8 = \sigma_8 \sqrt{\Omega_{\rm m}/0.3}$ with a mean value of$0.790^{+0.018}_{-0.014}$. The mean marginal is lower than the maximum aposteriori estimate, $S_8=0.801$, owing to skewness in the marginaldistribution and projection effects in the multi-dimensional parameter space.Our results are consistent with $S_8$ constraints from observations of thecosmic microwave background by Planck, with agreement at the $1.7\sigma$ level.We use a Hybrid analysis pipeline, defined from a mock survey study quantifyingthe impact of the different analysis choices originally adopted by each surveyteam. We review intrinsic alignment models, baryon feedback mitigationstrategies, priors, samplers and models of the non-linear matter powerspectrum.

DES Y3 + KiDS-1000: Consistent cosmology combining cosmic shear surveys