Description and specifications of a new and distinct blackberry cultivar named ‘APF-45’ which originated from seed produced by a hand pollinated cross of Ark. Selection APF-1 (non-patented, unreleased genotype)×APF-12 (U.S. Plant Pat. No. 16,989) is provided. This new blackberry cultivar can be distinguished by its very firm fruit with excellent postharvest handling potential, medium-large size, attractive fruit appearance, very good flavor, excellent plant health, and cane erectness.