Extensively drug-resistant Neisseria gonorrhoeae (XDR-NG) strains with resistance to the last remaining first-line treatments (ceftriaxone monotherapy or combined with azithromycin) represent the emerging threat of untreatable gonorrhea. We present the complete reference genome sequence of the XDR-NG strain AT159, with ceftriaxone and high-level azithromycin resistance, from Austria.