This article presents the results of a realistic global fit of the Lagrangian parameters of the Minimal Supersymmetric Standard Model with no assumptions on the SUSY breaking mechanism using the fit program Fittino. The fit is performed using the precision of future mass measurements of superpartners at the LHC and mass and polarized topological cross-section measurements at the ILC. Higher order radiative corrections are accounted for wherever possible to date. Results are obtained for a modified SPS1a MSSM benchmark scenario (general MSSM without assumptions on the breaking mechanism) and for a specific mSUGRA scenario. Exploiting a simulated annealing algorithm, a stable result is obtained without any {it a priori} assumptions on the fit parameters. Most of the Lagrangian parameters can be extracted at the percent level or better if theoretical uncertainties are neglected. Neither LHC nor ILC measurements alone will be sufficient to obtain a stable result.