In this paper we summarize the measurement of the electromagnetic (EM) scale calibration constant for 11% of the Tile Calorimeter modules exposed to electron and muon test beams at CERN SPS accelerator. The Tile Calorimeter modules are currently installed in the ATLAS detector. The analysis presented in this paper takes into account the recent improvements in the Tile Calorimeter cesium calibration, charge injection system calibration and Fit Method energy reconstruction. The overall conversion factor between the measured charge and the energy deposited by measured particles for Tile Calorimeter cells is 1.050pm0.003~pC/GeV, with spread of 2.4pm0.1%. We discuss in detail the sources of uncertainties of EM scale calibration constant. We also show, that after inter-calibrating all the Tile Calorimeter cells with a~radioactive cesium source and setting the EM scale in the first calorimeter sampling with electron beams, the values of signals measured in the second and third calorimeter sampling need to be increased by 1--9% to keep the EM scale uniform in the whole calorimeter
