To date, no clear specific cognitive predictors of speech perception outcome in older adult cochlear implant (CI) users have yet emerged. The aim of this prospective study was to increase knowledge on cognitive and clinical predictors of the audiological outcome in adult cochlear implant users. A total of 21 patients with post-lingual deafness, who were candidates for cochlear implantation, were recruited at the Department of Ear, Nose and Throat, University of Torino (Italy) and subjected to a pre-operatory neuropsychological assessment (T0) and an audiological examination after 12 months of implantation (T12). Patients who, at T12, had a 60 dB verbal recognition above 80%, were younger (z = −2.131, p = 0.033) and performed better in the Verbal Semantic Fluency Test at T0 (z = −1.941, p = 0.052) than subjects who had a 60 dB verbal recognition at T12 below 80%. The most significant predictors of the CI audiological outcome at T12 were age (β = −0.492, p = 0.024) and patients’ TMT-A performance at baseline (β = −0.486, p = 0.035). We conclude that cognitive processing speed might be a good predictor of the level of speech understanding in older adult patients with CI after one year of implantation.