After six months, they could be moved to the UK.
Others in the group are being offered financial incentives to go to Sri Lanka where they say they face persecution.
In 2021, dozens of Tamils became the first people ever to claim asylum on Diego Garcia after their boat ran into trouble.
The territory’s unusual status led to a long legal dispute, with the UK government saying that bringing them to Britain risked creating a “backdoor migration route”.
The offer to the migrants, by British officials on the island, came after the UK announced it was handing sovereignty of the British Indian Ocean Territory (Biot), which includes Diego Garcia, to Mauritius.
The military base, however, will remain on the island.