Electrically, yes. A ceiling fan works just like a typical light fixture (in most cases), when you flip the switch the fan turn on (assuming the pull chain switch is in the proper state).
Installing a ceiling fan is the same procedure as hooking up any light fixture (Turn off the breaker first!), simply connect the black (hot) from the ceiling (should be controlled by the switch) to the black on the ceiling fan. Then connect the white (neutral), to the white on the ceiling fan. If the fan has a light kit you'll notice an extra blue wire (color may vary), hook this one up to the black (hot) from the ceiling along with the black from the fan. Then twist all bare/green (ground) wires together, and ground them as per the direction that came with the fan.
Structurally, maybe not. Keep in mind the electrical box that is currently there was designed to hold the weight of a typical light fixture (a couple pounds max), not a ceiling fan (15-50 lbs). It's possible the electrical box itself will hold the fan, but I wouldn't put any of my family members under it. they make "Old work ceiling fan boxes", that come with a brace that spans between the joists to hold the extra weight of a ceiling fan. The brace bar expands and contracts, so you can stick it up in the hole (after you remove the old electrical box) and then expand it until it bites into the joists. Then you'll hang the new electrical box from this brace, and install the fan as usual.
