From the ROTJ screenplay:

Obi-Wan Kenobi said:

When your father left, he didn't know your mother was pregnant. Your mother and I knew he would find out eventually, but we wanted to keep you both as safe as possible, for as long as possible. So I took you to live with my brother Owen on Tatooine... and your mother took Leia to live as the daughter of Senator Ogana, on Alderaan.

Of course, how a faneditor would go about communicating all that to the viewer is another matter entirely...