A universal approach to the construction of antibody-drug conjugates (ADCs) has been developed. It relies on periodate oxidation of naturally present glycans of immunoglobulin G, followed by oxime ligation and, optionally, copper(I)-catalyzed alkyne-azide cycloaddition for conjugation with a toxic payload. The introduction of highly absorbing cyanine dyes into the linker allows for facile determination of the drug-antibody ratio. We applied this methodology to the synthesis of cytotoxic conjugates of an antibody against the tumor-associated antigen PRAME with doxorubicin and monomethyl auristatin E (MMAE). The resultant conjugates retained their affinity to a large extent, yet their cytotoxicity in vitro varied dramatically: while the doxorubicin-based conjugate did not produce any effect on cells, the MMAE-based one demonstrated specific activity against PRAME-expressing cancer cell lines. Importantly, the latter conjugate constitutes the first reported example of a PRAME-targeting ADC.