The contract is worth about $870 million, with options exceeding that of the original contract.
"We are proud to supply world class ammunition that is both environmental friendly and fully satisfies the customer's demands for operational function," said Edgar Fossheim, president and chief executive officer of Nammo.
Nammo said its lead-free NM255 bullet releases lower levels of dust particles and exhaust gases.
"We have developed new, improved lead-free ammunition of world class quality," said a company official. "For Nammo, it is important to be at the forefront of future environmental requirements and to develop products that are less harmful to the health of the users and cause less damage to the environment."
The ammunition will be manufactured at a company facility in Sweden.
Sales of the lead-free ammunition to other military forces worldwide are being eyed by the company.