The car, a more performance-orientated version of the standard Veloster, is powered by a 1.6-litre direct-injection turbocharged engine which Hyundai says is perfect for aftermarket tuners.
The firm says it has enhanced the standard Veloster with a tuned chassis, new bodywork and a new six-speed manual transmission. On the outside, the model gets a new front splitter and new R-Spec badging at the rear. Inside, special red leather trim features with red cloth sports seats and bespoke R-Spec mats.
Hyundai says that in keeping with a focus on pure driving, some standard equipment from the standard Turbo model - including push-button start, an automatic driver's window, and heater leather seats - have been left out from the R-Spec model.
A new Torque Vectoring Control system has been added however, which manages the on-board ESC and traction settings to improve cornering response and handling.
The Veloster Turbo R-Spec is the fourth model in Hyundai's range to carry the R-Spec moniker, which has previously been applied to the Genesis and Genesis Coupe models.
Production will begin in December this year with the first customer deliveries taking place in February 2014. The model will become the lowest-priced option in the Veloster Turbo range, with prices starting at the US equivalent of £13,692.