Will oral bc stop depo bleeding?

I'm in my third month since taking the depo shot, and I'm due for another one March 12th. However. I won't be getting it again. I've been bleeding for nearly a month straight, dark brown, light, stringy blood. I'm frustrated with it. I got checked by my doctor, and she says its just a side effect of the depo. She prescribed oral contraceptives to regulate my period again. I started them today. Will the pills cut off the bleeding? If so, how soon?