One of the most important representatives of electrically conductive polymers is poly(3,4-ethylenedioxythiophene) (PEDOT), which, due to its properties such as electrical conductivity, corrosion resistance, chemical stability, biocompatibility, and ease of processing, has found applications in various fields, including wearable electronics, biomedical devices, sensors, and batteries. Its mechanical properties such as stiffness and inflexibility, as well as its electrical conductivity, can be improved by chemical modification with other polymers to approach the potential application of this conductive polymer in wearable electronics, where electronic components are embedded in flexible substrates. Flexibility of the conductive polymer PEDOT was improved in this work by grafting side branches of ethylene glycol (EG) onto the main chain of PEDOT by atom transfer radical polymerization (ATRP). The synthesis of the PEDOT-g-PEG graft copolymer was carried out in three steps. In the first step, the bromine-functionalized thiophene monomer (ThBr) was synthesized. In the second step, two macroinitiators with different proportions of ThBr were synthesized by chemical oxidation polymerization, and in the third step, a non-covalently crosslinked graft copolymer with different proportions of macroinitiators and poly(ethylene glycol) methacrylate (PEG-MA) was synthesized. The success of the synthesis of the obtained products was checked by Fourier transform infrared spectroscopy (FTIR) and nuclear magnetic resonance (NMR). The morphology was studied by scanning electron microscope (SEM). Thermal properties and stability were tested using thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). The crosslinking of the final products was tested with a swelling test. FTIR and NMR analysis proved the successful synthesis of the products. The results of the DSC proved that by grafting the side branches of PEG-MA, the glass transition temperature of the final product is reduced to below the body temperature of 37 °C, which enables potential application in wearable electronics because the polymer in contact with the skin would be flexible enough for application. The cross-linking of the graft copolymer was proven by the swelling test.