The move sees the German maker catching up with Toyota, Honda and Hyundai, who already have fuel-cell cars in their ranges.
Fuel cells use hydrogen to create electricity and with worries about the limited range of pure electrics, several manufacturers are hedging their bets by working on fuel-cell solutions.
The GLC F-Cell was seen at last year's Frankfurt car show and the production version is very similar in appearance.
Dealerships in Germany will be the first to get the car and only for comprehensive full-service lease schemes, Mercedes-Benz said without revealing further details. That means, for now, customers will not be able to buy the car outright.
Full lease packages typically include fuel, emergency roadside repairs, preventive maintenance, garage services and a courtesy vehicle when the car is being worked on. The deal usually includes wide-ranging guarantees.
Mercedes-Benz said the F-Cell will be reliable enough for daily use. It will be assembled at the company's Bremen factory in northern Germany.
At first glance, the fuel-cell GLC is hard to tell apart from regular editions of the popular SUV. The grille has a blue accent, the badge reads F-Cell and there are dedicated alloy wheels.
Inside, the fuel-cell GLC gets the standard cabin, which now features a 12.3-inch digital instrument cluster and a slightly smaller screen.
The F-Cell's powertrain is the most interesting part. The car is a hydrogen-electric plug-in hybrid which means the 200-horsepower electric motor gets most of its power from the fuel cell which produces electricity from hydrogen. Water vapour is the only tailpipe emission.
The 4.4 kilos of hydrogen stored in two crash-protected tanks and can propel the car for 447km, the maker says. When the hydrogen runs out, the 13.8 kilowatt-hour motor and batteries - which can be charged externally - provide a further range of 49km.
Filling the hydrogen tanks takes around three minutes. This is about the time it takes to refuel a petrol or diesel car.
The F-Cell is unlikely to sell in large numbers since hydrogen infrastructure around the world is still in its infancy.
There are only 50 refuelling points in Mercedes' home of Germany, although the company says this number will double by next year and rise to 400 by 2023.
