Newly synthesized mRNAs are exported from the nucleus to cytoplasm with a 5′-cap structure bound by the nuclear cap-binding complex (CBC). During or after export, the CBC should be properly replaced by cytoplasmic cap-binding protein eIF4E for efficient protein synthesis. Nonetheless, little is known about how the replacement takes place. Here, we show that double-stranded RNA-binding protein staufen1 (STAU1) promotes efficient replacement by facilitating an association between the CBC–importin α complex and importin β. Our transcriptome-wide analyses and artificial tethering experiments also reveal that the replacement occurs more efficiently when an mRNA associates with STAU1. This event is inhibited by a key nonsense-mediated mRNA decay factor, UPF1, which directly interacts with STAU1. Furthermore, we find that cellular apoptosis that is induced by ionizing radiation is accompanied by inhibition of the replacement via increased association between STAU1 and hyperphosphorylated UPF1. Altogether, our data highlight the functional importance of STAU1 and UPF1 in the course of the replacement of the CBC by eIF4E, adding a previously unappreciated layer of post-transcriptional gene regulation.