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Using the astraeus (seminumerical rAdiative tranSfer coupling of galaxy formaTion and Reionization in N -body dark matter simUlationS) framework, we explore the impact of environmental density and radiative feedback on the assembly of galaxies and their host haloes during the Epoch of Reionization. The astraeus framework allows us to study the evolution of galaxies with masses (⁠|$10^{8.2}\,\rm M_\odot \lt M_{\rm h}\lt 10^{13}\,\rm M_\odot$|⁠) in a wide variety of environment [−0.5 < log (1 + δ) < 1.3 averaged over (2 cMpc)3]. We find that: (i) there exists a mass- and redshift- dependent 'characteristic' environment [ |${\rm log}\, (1+\delta _a(M_{\rm h}, z)) = 0.021\times (M_{\rm h}/\rm M_\odot)^{0.16} + 0.07 z -1.12$|⁠ , up to |$z$| ∼ 10] at which galaxies are most efficient at accreting dark matter, e.g at a rate of |$0.2{{\ \rm per\ cent}}$| of their mass every Myr at |$z$|  = 5; (ii) the number of minor and major mergers and their contributions to the dark matter assembly increases with halo mass at all redshifts and is mostly independent of the environment; (iii) at |$z$|  = 5 minor mergers contribute slightly more (by up to |$\sim 10{{\ \rm per\ cent}}$|⁠) to the dark matter assembly while for the stellar assembly, major mergers dominate the contribution from minor mergers for |$M_{\rm h}\lesssim 10^{11.5}\rm\, M_\odot$| galaxies; (iv) radiative feedback quenches star formation more in low-mass galaxies (⁠|$M_{\rm h}\lesssim 10^{9.5}\rm\, M_\odot$|⁠) in over-dense environments [log(1 + δ) > 0.5]; dominated by their major branch, this yields star formation histories biased towards older ages with a slower redshift evolution. [ABSTRACT FROM AUTHOR]