We study the Berezinskii-Kosterlitz-Thouless transition in a weakly interacting 2D quantum Bose gas using the concept of universality and numerical simulations of the classical |ψ|4 model on a lattice. The critical density and chemical potential are given by relations nc = (mT/2πħ2)ln(ξħ2/mU) and μc = (mTU/πħ2)ln(ξμħ2/mU), where T is the temperature, m is the mass, and U is the effective interaction. The dimensionless constant ξ = 380±3 is very large and thus any quantitative analysis of the experimental data crucially depends on its value. For ξμ our result is ξμ = 13.2±0.4. We also report the study of the quasicondensate correlations at the critical point.