Yep, you can just copy the entire Origin Games\Battlefield 4 folder to the new computer. Place it in the new computer's Origin Games or a location of your choice *see image below if non-default location is used*
It will say "Download" but skip the actual downloading part and jump straight to installing.
If you put Origin Games in a non-default location, you just need to go to Origin's settings and change it's Downloaded Games location.
I would do a "repair" from Origin once it's finished just for good measure.
