The tsunami-generated magnetic field is a magnetic field that show up with the moving of tsunami. In the previous studies, researchers claimed that the tsunami-generated magnetic field arrives earlier than the tsunami sea level change based on analytical solutions and numerical simulations. In this paper, we used the world's first simultaneous data of sea level change and magnetic field in the 2009 Samoa and 2010 Chile tsunamis to study the relation between these two physical quantities. We found that the vertical component of tsunami magnetic field arrives earlier than the sea level change. Moreover, the horizontal component of tsunami magnetic field arrives even earlier than the vertical component. The tsunami magnetic field was also revealed that it can be used to estimate the tsunami wave height very accurately. We investigated the observed tsunami magnetic field by our 3-D time-domain simulation. However, the currently existing tsunami source models were unable to reproduce the observation in our research area. We confirmed that a better source model can improve the simulation. It follows that our high precision tsunami wave height data converted from the magnetic field should be used to construct a better tsunami source model.