The UK and Mauritius are now finalising the agreement, which includes a lease-back arrangement for the Diego Garcia airbase.
The deal has faced criticism due to its potential cost – up to £18 billion, according to reports – and the perceived unnecessary lease of a base the UK already owns.
The International Court of Justice earlier ruled that the archipelago belongs to Mauritius.
The Chagos Islands represent an important part of UK-US security plans because of the airbase, which is strategically important for both countries’ militaries.