The initial and present-day mass functions (ICMFs and PDMFs, respectively) of the Galactic globular clusters (GCs) are constructed based on their observed luminosities, the stellar evolution and dynamical mass-loss processes, and the mass-to-light ratio (M/L). Under these conditions, a Schechter-like ICMF is evolved for approximately a Hubble time and converted into a luminosity function (LF), which requires finding the values of five free parameters: the mean GC age (), the dissolution time-scale of a 105-M⊙ cluster (τ5), the exponential truncation mass () and two M/L parametrizing constants. This is achieved by minimizing the residuals between the evolved and observed LFs, with the minimum residuals and realistic parameters obtained with M/Ls that increase with luminosity (or mass). The optimum PMDFs indicate a total stellar mass of ∼4 × 107 M⊙ still bound to GCs, representing ∼15 per cent of the mass in clusters at the beginning of the gas-free evolution. The corresponding ICMFs resemble the scale-free MFs of young clusters and molecular clouds observed in the local Universe, while the PDMFs follow closely a lognormal distribution with a turnover at M⊙. For most of the GC mass range, we find an M/L lower than usually adopted, which explains the somewhat low . Our results confirm that the M/L increases with cluster mass (or luminosity), and suggest that GCs and young clusters share a common origin in terms of physical processes related to formation.