A new biophenolic secoiridoid was identified in Australian Frantoio olive mill waste (OMW) extracts. Isolation, purification, and structure elucidation were performed. Hydroxytyrosyl acyclodihydroelenolate, the first nonaldehydic acyclic secoiridoid, is reported. A second compound was identified as p-coumaroyl-6′-secologanoside (comselogoside), and although it has been identified recently in OMW and leaves, this is the first time it has been identified in both OMW and olive fruits. UV, mass spectral, and NMR data are given for both compounds. The two compounds were quantified by HPLC-DAD, and their antioxidant potential was assessed against the classical olive biophenols, hydroxytyrosol and oleuropein, by the in vitro DPPH radical scavenging assay.