Replying to Going to Africa, Need a Lens

For my graduation present from college my aunt said she would take me anywhere in the world so we're going on safari in Africa at the end of May. Currently I have a t3i body with the kit lens (18-55) and a 10-22 Canon lens. Obviously those won't be good for photographing lions and what not so I need something with some zoom.

I was thinking about the Canon F4L 70-200 but I am not sure if that's enough zoom. Anyone have any experience with real wildlife photography? Is 200 enough?

My budget is like 800 or so but thats a bit flexible if there is something awesome for a little more.

Not sure if this matters but I'll probably upgrade to the t6s before we leave. Hoping to get part of that paid for for my birthday.

Thank you!