The RNA exosome is a conserved degradation machinery, which obtains full activity only when associated with cofactors. The most prominent activator of the yeast nuclear exosome is the RNA helicase Mtr4p, acting in the context of the Trf4p/Air2p/Mtr4p polyadenylation (TRAMP) complex. The existence of a similar activator(s) in humans remains elusive. By establishing an interaction network of the human nuclear exosome, we identify the trimeric Nuclear Exosome Targeting (NEXT) complex, containing hMTR4, the Zn-knuckle protein ZCCHC8, and the putative RNA binding protein RBM7. ZCCHC8 and RBM7 are excluded from nucleoli, and consistently NEXT is specifically required for the exosomal degradation of promoter upstream transcripts (PROMPTs). We also detect putative homolog TRAMP subunits hTRF4-2 (Trf4p) and ZCCHC7 (Air2p) in hRRP6 and hMTR4 precipitates. However, at least ZCCHC7 function is restricted to nucleoli. Our results suggest that human nuclear exosome degradation pathways comprise modules of spatially organized cofactors that diverge from the yeast model.