It's a common phrase that means "I've/ We've satisfactorily finished this job," or "This remedy will solve the problem." "That ought to take care of it" is a variation. You might hear this after a long period of hard work, i.e. struggling with a virus-infected computer or some other kind of repair work. "I've wiped the hard drive and reinstalled all your software. That ought to do it." (I don't know much about computers, sorry!)
Or someone might add it after suggesting a course of action: "If your children misbehave, try taking away their television for a week. That ought to do it."
It implies that from now on, things will proceed smoothly.