New quaternized chitosan derivatives HT-TMC were synthesized as a result of copper catalyzed azide-alkyne [3 + 2] cycloaddition (CuAAC). The structure of the HT-TMC was verified by 2D NMR. The synthesis was carried out as a result of the formation of Cu(I) in situ, under the action of ultrasound in aerobic conditions in the presence of acetic acid and metallic copper (copper turnings). The new derivatives were characterized by increased pH range of solubility (DS range 18–76%) and the presence of antibacterial and fungicidal activities. The proposed catalytic system makes it possible to easily and efficiently obtain new derivatives of chitosan as a result of ultrasound-promoted CuAAC.