The relationship between the atmospheric concentration of cosmogenic isotopes, the change of solar activity and hence secondary neutron flux has already been proven. The temporal atmospheric variation of the most studied cosmogenic isotopes shows a significant anti-correlation with solar cycles. However, since artificial tritium input to the atmosphere due to nuclear-weapon tests masked the expected variations of tritium production rate by three orders of magnitude, the natural variation of tritium in meteoric precipitation has not previously been detected. For the first time, we provide clear evidence of the positive correlation between the tritium concentration of meteoric precipitation and neutron flux modulated by solar magnetic activity. We found trends in tritium time series for numerous locations worldwide which are similar to the variation of secondary neutron flux and sun spot numbers. This variability appears to have similar periodicities to that of solar cycle. Frequency analysis, cross correlation analysis, continuous and cross wavelet analysis provide mathematical evidence that the correlation between solar cycle and meteoric tritium does exist. Our results demonstrate that the response of tritium variation in precipitation to the solar cycle can be used to help us understand its role in the water cycle.