Due to its high coding density and longevity, DNA is a compelling data storage alternative. However, current DNA data storage systems rely on the de novo synthesis of enormous DNA molecules, resulting in low data editability, high synthesis costs, and restrictions on further applications. Here, we demonstrate the programmable assembly of reusable DNA blocks for versatile data storage using the ancient movable type printing principle. Digital data are first encoded into nucleotide sequences in DNA hairpins, which are then synthesized and immobilized on solid beads as modular DNA blocks. Using DNA polymerase-catalyzed primer exchange reaction, data can be continuously replicated from hairpins on DNA blocks and attached to a primer in tandem to produce new information. The assembly of DNA blocks is highly programmable, producing various data by reusing a finite number of DNA blocks and reducing synthesis costs (∼1718 versus 3000 to 30,000 US$ per megabyte using conventional methods). We demonstrate the flexible assembly of texts, images, and random numbers using DNA blocks and the integration with DNA logic circuits to manipulate data synthesis. This work suggests a flexible paradigm by recombining already synthesized DNA to build cost-effective and intelligent DNA data storage systems.