The new vehicle-mounted radar will be able to spot threats up to 75 miles away and the first systems will be delivered before the end of the year.
The Defence Secretary earlier this year said Britain would strengthen the islands' defences amid reports Argentina was trying to update its aged air force with Russian or Chinese jets.
Michael Fallon warned there was a "very live threat" to the islands.
He said: "It is our general view that the threat has not reduced. Argentina still, sadly, maintains its claim to the islands 30 or more years after the original invasion and the war and we have to respond to that."
The Ministry of Defence has already ordered new anti-aircraft missiles for the islands to one day replace its existing batteries.