Yes, if you keep the F-series mounts on the F-series. The bumper is the same, but the mounting brackets are different for Broncos.
^ (clickable on a computer with a monitor)
Unfortunately, the fasteners holding the brackets to the bumpers are VERY difficult to remove. The outboard nuts are 18mm, but the exposed bolts are carriage-type (square shank below the head) and commonly spin in the bumper skin. If you can get the bumper on the ground, soak all 6 with penetrating oil, put down a 2x4, stand inside the bumper so the bolt head is pressed against the wood, and use a long extension to completely remove the nut from the bolt. It's shown at the top of this pic, just R of center (the pic is huge, so you have to view it on a fullsize monitor & pan across):
But the outboard brackets MIGHT be the same, so check before doing that. The inboard brackets are certainly different, and the nuts are crimped into a thin sheet-metal stay to make installation easier. But since they're now 20 years old with corrosion, dirt, & road grime; the stays aren't strong enough to break the bolts loose - they'll twist & break. And they're so far down on the nuts' hexes that it's very difficult to get a wrench on. Plus, the corners of the hexes are shaved down to stake the stays onto the nuts, which makes it even-harder to get a wrench on, even if you rip the stays off. So what I've found works best (usually) is vise-grips clamped onto the nuts' flanges, right against the bumper. In one case, I had to rip the thin stays off, and weld a heavier stay between the nuts. But that made the rest of the job much easier.