"Is the Canon 70-200MM, USM, IS, II, f2.8 lens compatible with my Canon EOS60D camera?"
Not only compatible but it is the very best lens made in this focal range. 
@ebiggs1 wrote:"Is the Canon 70-200MM, USM, IS, II, f2.8 lens compatible with my Canon EOS60D camera?"
Not only compatible but it is the very best lens made in this focal range.
Quite true. But if you expect to use that lens indoors on a 60D, it had better be in a very large room.
"... it had better be in a very large room."
Bob from Boston, I did not realize it was restricted to being used in rooms! 
@ebiggs1 wrote:"... it had better be in a very large room."
Bob from Boston, I did not realize it was restricted to being used in rooms!
Well, I didn't say it was. You cropped the word "indoors" out of that sentence. 
I've used my 70-200 outdoors (on the rocks at Acadia, for example), but I use it indoors more.
