The Storm Shadow, made by MBDA, is a long-range air-to-surface weapon for use against targets such as bridges, airfields, harbors.
The missiles were previously been deployed on Eurofighter's Tornado GR4 aircraft during operations over Iraq and Libya.
"Storm Shadow has a deserved reputation for accuracy and reliability," said British Minister for Defense Equipment Support and Technology Philip Dunne. "The integration of Storm Shadow onto RAF Typhoons is another powerful sign of our commitment to the continued capability development of this world class aircraft.
"The ability to prosecute stand-off targeting while maintaining control of the airspace will provide Typhoon with unique battle winning capability."
The agreement, worth about $205 million, signed on Tuesday is between Eurofighter GmbH, manufacturer of the Typhoon and Tornado, and the NATO Eurofighter Tornado Management Agency, on behalf of the partner nations.
The key partner nations in the Eurofighter program are Britain Italy, Spain and Germany. The Eurofighter consortium is made up of BAE Systems, Alenia Aermacchi and Airbus.
The missiles, which first became operational in 2002, will be integrated onto Typhoon Tranche 2 and Tranche 3 planes. The aircraft will enter service with the Royal Air Force in 2018.