It certainly will fit -- the tire is somewhat smaller, so you won't have any rubbing problems whatsoever.

When you go to a 1 cm wider, 0.1 aspect ratio (or ten point) lower profile tire on a taller rim, such as going from 185/70-14 to 195/60-15, everything is in balance: same overall diameter (and speedo/odometer accuracy), almost the same load rating. This is called a Plus One upgrade. But you're going to a wider, lower profile tire on the same size rim, so you have to be aware:

Pros:
1) somewhat better steering response and handling, assuming the tire has the same construction and traction or speed rating (e.g., H), because it has a lower and therefore stiffer sidewall. However, your tire width to wheel width is larger (this has to do with tire-wheel fitment), so it may just be even -- wider tires deserve wider wheels, but the difference is very modest in this case.
2) theoretically, you'll have a modest increase in torque* to the drive wheels, although I doubt you'll notice it.
[ * because the tire has a 4% (~1") smaller diameter, that will lower your overall final drive ratio by the same amount. It's as if your rear axle ratio was lowered.]

Cons:
1) your new tires will have a lower load rating (e.g., 89 or 90 or whatever) -- don't load your car to capacity and drive it fast, at least without raising your tire pressure to compensate.
2) Your speedo and odometer will be off by that same 4% -- i.e., when your odometer says that you've driven 100 miles, you've really only driven 96 miles; likewise, when you speedo says that you're driving 50 mph, you're really only driving 48 mph.
3) Your car will sit 0.5" lower (i.e., half of the reduced tire diameter): good (but hardly noticeable) for improved handling (i.e., a lower roll center); but bad for clearance from road debris, potholes, etc., as that 1/2" may be the difference between safe passage and ripping off or smashing something underneath your car.

And it's hard to predict how it will affect your fuel mileage. It can be argued that lower profile tires and their stiffer sidewall requires more fuel to turn them; and lower final drive ratios tend to increase consumption because the engine must turn more times per mile (or per minute, for a given true road speed). But the lower final drive ratio might alternatively help your mileage by making it easier for the engine to propel the car.