Nanocomposites of poly(lactic acid) (PLA)/poly(butylene adipate-co-terephthalate) (PBAT) blends with multiwalled carbon nanotubes (MWCNTs) were prepared and their morphology, as well as electrical, mechanical, and thermal properties were investigated. The motivation of this work is to prepare electrically conductive and environmentally benign polymer nanocomposites using biodegradable PLA/PBAT blends. The composites were characterized by Fourier transform infrared (FTIR) spectroscopy, scanning and transmission electron microscopy, tensile and microindentation tests, and thermogravimetric analyses (TGA). Volume resistivity and resistance to tensile deformation were measured for electrical characterization. The nanocomposites films were integrated into an electrical circuit to confirm their electrical conductivity. The FTIR spectra revealed the physical mixing between the polymer matrix and the filler. TEM micrographs suggested selective localization of MWCNTs in the PBAT phase with partial agglomeration forming a co-continuous morphology. TGA and derivative thermogravimetric curves suggested the overall decreasing thermal stability of composites than pure polymer blends regardless of the effects on individual blend components. A relatively low electrical percolation threshold (around 1 wt% of the fillers) compared to the literature works was achieved. Increasing electrical resistance of nanocomposites upon tensile deformation suggested their possibility of piezoresistive properties. Furthermore, the overall mechanical performance (i.e., elastic modulus, tensile strength, and hardness) of the materials was found to improve with increasing filler content.