Meson Green's functions and decay constants fΓ in different channels Γ are calculated using the field correlator method. Both, spectrum and fΓ, appear to be expressed only through universal constants: the string tension σ, αs, and the pole quark masses. For the S-wave states the calculated masses agree with the experimental numbers within ±5MeV. For the D and Ds mesons the values of fP(1S) are equal to 210(10) and 260(10)MeV, respectively, and their ratio fDs/fD=1.24(3), agrees with a recent CLEO experiment. The values fP(1S)=182, 216, 438 MeV are obtained for the B, Bs, and Bc mesons with the ratio fBs/fB=1.19(2) and fD/fB=1.14(2). The decay constants fP(2S) for the first radial excitations as well as the decay constants fV(1S) in the vector channel are also calculated. The difference of about 20% between fDs and fD, fBs and fB directly follows from our analytical formulas. © 2007 The American Physical Society.