We analyze Brans-Dicke gravity with a cosmological constant, $Lambda$, and cold dark matter (BD-$Lambda$CDM for short) in the light of the latest cosmological observations on distant supernovae, Hubble rate measurements at different redshifts, baryonic acoustic oscillations, large scale structure formation data, gravitational weak-lensing and the cosmic microwave background under full Planck 2015 CMB likelihood. Our analysis includes both the background and perturbations equations. We find that BD-$Lambda$CDM is observationally favored as compared to the concordance $Lambda$CDM model, which is traditionally defined within General Relativity (GR). In particular, some well-known persisting tensions of the $Lambda$CDM with the data, such as the excess in the mass fluctuation amplitude $sigma_8$ and specially the acute $H_0$-tension with the local measurements, essentially disappear in this context. Furthermore, viewed from the GR standpoint, BD-$Lambda$CDM cosmology mimics quintessence at $gtrsim3sigma$ c.l. near our time.
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