The Falkland Islands legislative assembly said Baroness Thatcher's "friendship and support" to the territory would be "sorely missed".
Assembly member Mike Summers said: "It is with great sadness that we received news of the death of Baroness Thatcher this morning.
"She will be forever remembered in the Islands for her decisiveness in sending a task force to liberate our home following the Argentine invasion in 1982."
More top news
Soldiers and veterans are being encouraged to "take back control" and vote to leave the EU by a number of senior military officers.
The 60-year-old, whose daughter died of cancer, is taking her case to the Court of Appeal after losing a High Court action.
Leicester City star Jamie Vardy will marry his fiancee Rebekah Nicholson in a lavish ceremony on Wednesday.