Quantitative spectroscopy of luminous BA-type supergiants offers a high potential for modern astrophysics. Detailed studies allow the evolution of massive stars, galactochemical evolution, and the cosmic distance scale to be constrained observationally. A detailed and comprehensive understanding of the atmospheres of BA-type supergiants is required in order to use this potential properly. The degree to which we can rely on quantitative studies of this class of stars as a whole depends on the quality of the analyses for benchmark objects. We constrain the basic atmospheric parameters and fundamental stellar parameters, as well as chemical abundances of the prototype A-type supergiant Deneb to unprecedented accuracy by applying a sophisticated analysis methodology, which has recently been developed and tested. The analysis is based on high-S/N and high-resolution spectra in the visual and near-IR. Stellar parameters and abundances for numerous astrophysically interesting elements are derived from synthesis of the photospheric spectrum using a hybrid non-LTE technique, i.e. line-blanketed LTE model atmospheres and non-LTE line formation. Multiple metal ionisation equilibria and numerous hydrogen lines from the Balmer, Paschen, Brackett, and Pfund series are utilised simultaneously for the stellar parameter determination. The stellar wind properties are derived from Hα line-profile fitting using line-blanketed hydrodynamic non-LTE models. Further constraints come from matching the photospheric spectral energy distribution from the UV to the near-IR L band. The atmospheric parameters of Deneb are tightly constrained: effective temperature Teff=8525±75K, surface gravity logg=1.10±0.05, microturbulence ξ=8±1km/s, macroturbulence, and projected rotational velocity vsini are both 20±2km/s. The abundance analysis gives helium enrichment by 0.10dex relative to solar and an N/C ratio of 4.44±0.84 (mass fraction), implying strong mixing with CN-processed matter. The heavier elements are consistently underabundant by ∼0.20dex compared to solar. Peculiar abundance patterns, which were suggested in previous analyses cannot be confirmed. Accounting for non-LTE effects is essential for removing systematic trends in the abundance determination, for minimising statistical 1σ-uncertainties to ≲10-20% and for establishing all ionisation equilibria at the same time. A luminosity of (1.96±0.32)x105L☉, a radius of 203±17R☉, and a current mass of 19±4M☉ are derived. Comparison with stellar evolution predictions suggests that Deneb started as a fast-rotating late O-type star with MZAMS≃23M☉ on the main sequence and is currently evolving to the red supergiant stage.