The Norwegian company said the award for Protector "Nordic" Remote Weapon Stations is worth more than $64.3 million.
Delivery of the systems will start from the middle of next year.
"Our systems have been used under extreme conditions for many years and have proven to be a valuable asset for our customers and the soldiers serving in the field," says Egil Haugsdal, president of Kongsberg Protech Systems.
"These two customer nations are strategically important to Kongsberg as key Nordic nations. Cooperation with both Norway and Sweden is an important focus in the company and we are looking forward to executing this program together with our customers."
Use of the systems allows troops to operate vehicle weapons while in the vehicle.
Details on the number of systems to be delivered to Norwegian and Swedish forces weren't disclosed.
Kongsberg said it has been producing remote weapons stations for more than decade.