Meson Green's functions and decay constants f Γ in different channels Γ are calculated using the Field Correlator Method. Both, spectrum and f Γ , appear to be expressed only through universal constants: the string tension σ, α s , and the pole quark masses. For the S-wave states the calculated masses agree with the experimental numbers within ±5 MeV. For the D and D s mesons the values of f P (1S) are equal to 210(10) and 260(10) MeV, respectively, and their ratio f Ds /f D =1.24(3) agrees with recent CLEO experiment. The values f P (1S) = 182, 216, 438 MeV are obtained for the B, B s , and B c mesons with the ratio f Bs /f B =1.19(2) and f D /f B =1.14(2). The decay constants f P (2S) for the first radial excitations as well as the decay constants f V (1S) in the vector channel are also calculated. The difference of about 20% between f Ds and f D , f Bs and f B directly follows from our analytical formulas.