Intrinsically disordered proteins (IDPs) are involved in a wide range of regulatory processes in the cell. Owing to their flexibility, their conformations are expected to be particularly sensitive to the crowded cellular environment. Here we use single-molecule Förster resonance energy transfer to quantify the effect of crowding as mimicked by commonly used biocompatible polymers. We observe a compaction of IDPs not only with increasing concentration, but also with increasing size of the crowding agents, at variance with the predictions from scaled-particle theory, the prevalent paradigm in the field. However, the observed behavior can be explained quantitatively if the polymeric nature of both the IDPs and the crowding molecules is taken into account explicitly. Our results suggest that excluded volume interactions between overlapping biopolymers and the resulting criticality of the system can be essential contributions to the physics governing the crowded cellular milieu.