"Sen özür dileyince ben mutlu oldum". ("When you apologized, I became happy)".
The English translation sounds somewhat awkward and is not something naturally said. In meaning, it would be akin to, "Your apology made me happy". OR "I'm glad that you apologized". If you wanted to retain the exact sentence construct then I would suggest, "I felt happy when you apologized"/"Your apology made me feel happy".