Well, there are many possible authors for such a title. It might have been written by someone well-known in the literary world, or it could be the work of a relatively unknown but talented writer. The identity really depends on which particular 'Story of My Life' you're referring to.
Hard to say exactly who wrote it. There are countless books and works with similar titles. It could be someone from the past or a contemporary author. Without more specific details, it's tough to pin down the exact person.
It could be a variety of authors depending on the specific context. Maybe it was a famous novelist or an autobiographer.