  The well-known tensions on the cosmological parameters $H_0$ and $\sigma_8$
within the $\Lambda$CDM cosmology shown by the Planck-CMB and LSS data are
possibly due to the systematics in the data or our ignorance of some new
physics beyond the $\Lambda$CDM model. In this letter, we focus on the second
possibility, and investigate a minimal extension of the $\Lambda$CDM model by
allowing a coupling between its dark sector components (dark energy and dark
matter). We analyze this scenario with Planck-CMB, KiDS and HST data, and find
that the $H_0$ and $\sigma_8$ tensions disappear at 68\% CL. In the joint
analyzes with Planck, HST and KiDS data, we find non-zero coupling in the dark
sector up to 99\% CL. Thus, we find a strong statistical support from the
observational data for an interaction in the dark sector of the Universe while
solving the $H_0$ and $\sigma_8$ tensions simultaneously.
