The new model will go on sale next month, priced from £45,999, but Suzuki said that supply will be "very limited" in its first full year on sale.
Just one trim level will be available from launch, with leather upholstery, heated front and rear seats, a heated steering wheel, dual-zone automatic air conditioning, a powered tailgate and 9.0in touchscreen infotainment system equipped as standard.
It arrives following a recent agreement between Toyota and Suzuki to collaborate on selected models and, along with the Corolla Touring Sports-based Swace, gives an indication of how the two firms will seek to differentiate their own versions of shared models.
The Across bears a strong resemblance to the RAV4 but is set apart by an all-new front end that features Suzuki’s trademark large grille.
The differences between the two cars’ cabins are more subtle, with the Across having a largely identical interior, save for a new steering wheel. The RAV4’s 9.0in touchscreen features as standard and offers smartphone mirroring functionality.
The Across's electrified powertrain is carried over wholesale from the new RAV4 Plug-in Hybrid. It comprises a 173bhp 2.5-litre four-cylinder petrol engine and a pair of electric motors - one with 180bhp on the front axle and another with 54bhp at the rear - for a combined output of 302bhp, making it Suzuki's most powerful model to date by nearly 200bhp. The Across can accelerate from 0-62mph in 6.0sec and up to a top speed of 112mph.
The Across emits 22g/km of CO2 on the WLTP combined cycle, with its 18.1kWh battery allowing it to travel 46 miles on electricity alone. It’s expected to be able to reach speeds of up to 84mph in this mode, like the RAV4 PHEV.