The design, setup, and performance of a mass spectrometric system for the analysis of noble gas isotopes (He-3, He-4, Ne-20, Ne-21, Ne-22, Ar-36, Ar-40, Kr-84, Xe-136) and tritium (H-3) from water samples are described. The H-3 concentration is measured indirectly by the He-3 ingrowth from radioactive decay. After extraction, purification, and separation, the noble gases are measured in two noncommercial double-collector 90 degrees magnetic sector mass spectrometers. We present a new approach for the analysis of the heavy noble gas isotopes that enables, in principle, simultaneous measurement of Ar, Kr, and Xe. Typical precisions of the measurements of H-3, He, Ne, Ar, Kr, and Xe concentrations are +/-2.7%, +/-0.3%, +/-0.9%, +/-0.3%, +/-0.8%, and +/-1.0%, respectively. For the isotopic ratios He-3/He-4, Ne-20/Ne-22, and Ar-40/Ar-36 the typical precisions are +/-0.7%, +/-0.3%, and +/-0.2%. These values express the reproducibility of the measurement of an internal freshwater standard and include the overall stability of the system as well as of the extraction procedure. To verify the method, the noble gas concentrations of air-saturated water samples prepared under controlled conditions are compared with noble gas solubility data. The Ne-20/Ne-22 and Ar-36/Ar-40 fractionation during solution is estimated from 70 surface water samples to be -2.0 +/- 0.2 parts per thousand and -1.3 +/- 0.2 parts per thousand, respectively.