The first two helicopters will be delivered to Bolivia this year and the remaining four before 2016, for use in counter-narcotics, public security and disaster relief operations.
The value of the sale was not disclosed, but Airbus Helicopters said the deal includes a logistics package to sustain the Super Puma fleet.
The AS332 C1e is a twin-engine medium-size utility helicopter. It has a cruise speed of 152 mph, a range of more than 500 miles and a service ceiling of 20,000 feet.
"We are very proud to provide our air force with latest-generation multi-role aircraft that will enable us to successfully carry out our ongoing missions and face the challenges of the future," Air Chief Marshal Gen. Victor Hugo Meneses Gomez said. "Bearing in mind the extreme operating conditions in Bolivia, the Super Puma was chosen mainly because of its versatility, safety and, above all else, its ability to operate at high altitude."