In mitochondria cysteine desulfurase (Nfs1) plays a central role in the biosynthesis of iron-sulfur (FeS) clusters, cofactors critical for activity of many cellular proteins. Nfs1 functions both as a sulfur donor for cluster assembly and as a binding platform for other proteins functioning in the process. These include, not only the dedicated scaffold protein (Isu1) on which FeS clusters are synthesized, but also frataxin (Yfh1) and ferredoxin (Yah1). Yfh1 activates cysteine desulfurase enzymatic activity, while Yah1 supplies electrons for persulfide reduction. Yfh1 interaction with Nfs1 is well understood; that of Yah1 is not. Here, based on the results of biochemical experiments involving purified wild-type and variant proteins, we report that in Saccharomyces cerevisiae Yah1 and Yfh1 share an evolutionary conserved interaction site on Nfs1. Consistent with this notion each can displace the other from Nfs1, but are inefficient competitors when a variant with an altered interaction site is used. Thus, the binding mode of Yah1 and Yfh1 interacting with Nfs1 in mitochondria of S. cerevisiae resembles the mutually exclusive binding of ferredoxin and frataxin with cysteine desulfurase reported for the bacterial FeS cluster assembly system. Our findings are consistent with the generally accepted scenario that the mitochondrial FeS cluster assembly system was inherited from bacterial ancestors of mitochondria.