Ernest Rutherford is credited with discovering the principle of half-life. He made this discovery in 1907, originally calling it the "half-life period." The term was later shortened to "half-life" in the early 1950s. His work also encompassed the discovery of alpha and beta radiation.
While many scientists have since worked with and applied the concept of half-life in various fields (like carbon dating using the half-life of Carbon-14, or the study of different isotopes like Plutonium-239 and Plutonium-241 with their respective half-lives), the fundamental principle was established by Rutherford.