Turkish switched officially from the Arabic script to a Latin-based alphabet in Turkey in 1928. The reform was part of the modernization program associated with Mustafa Kemal Atatürk and the early Republic of Turkey.
Before the reform, Ottoman Turkish was written with a version of the Arabic script. That script could represent the language’s Arabic and Persian vocabulary, but it was poorly suited to Turkish vowel patterns. The new Turkish alphabet was based on Latin letters and adapted to represent Turkish pronunciation more consistently.
The alphabet reform was introduced through the Law on the Adoption and Implementation of the Turkish Alphabet, passed in November 1928. It formed part of broader language reforms that later encouraged replacing many Ottoman-era loanwords with words based on Turkish roots.
Azerbaijani, Uzbek, and Kazakh also experienced script changes, but their histories and dates differ. The question specifically concerns Turkey’s official 1928 transition, not every Turkic language that later adopted a Latin script.