Yes it will fit fine.
Up front, all you need are the rotors and cobra calipers. The 99+ brake lines were redesigned so that all 3 models (V6 GT Cobra) use the same lines. They will bolt to the calipers easily, but you will need the Cobra banjo bolts.
Out back is a little tougher. It will bolt fine but you need to pull the axles to change the caliper mount brackets. Pulling the axles is easy, but it's a messy job. You pull the axles out, swap the brackets, put the axles back on , then just slip on the rotors and bolt up the calipers. FYI, Cobras and GT's use the same calipers in the rear. The pads are different. If you want to make life easy, don't even disconnect your GT calipers, just hang them out of the way, then bolt them up with the correct Cobra brake pads. You will need to use the Cobra specific anti-moan bar in the rear.
You'll notice your car alreayd has the correct size brake dust sheilds. Ford made this swap very easy. I have the brake system of a 1998 Cobra on my '88 5.0 Mustang.