Crispin Blunt, a justice minister at Westminster, said payments to victims of atrocities overseas were to be limited to those "who have a clear and sufficient connection to the UK".
The scheme will only apply to six specific attacks since the start of 2002 and compensation – the scale of which is unknown – will be paid to those who "continue to have an ongoing disability as a direct result of the injuries they sustained".
Together with Bali and Mumbai, the relevant attacks are those at Sharm el Sheikh in Egypt in 2005, the bombing in Kusadasi, Turkey, in the same year, and those in 2006 at Dahab, Egypt, and Marmaris, Turkey.
Mr Blunt explained: "It is proportionate and necessary for the scheme to focus limited resources on those who have a clear and sufficient connection to the UK.
"Therefore, payments will be made to British, EU and EEA victims with a minimum of three years' residence in the UK immediately prior to a terrorist attack that is designated for the purposes of the ex gratia scheme."
Last night, Gregg McClymont, the Labour MP for Cumbernauld, who has been campaigning to secure compensation for victims of overseas terrorism, told The Herald the announcement was an important step forward for British victims of overseas terrorism.
He said: "It's now two years since cross-party agreement was reached on a scheme. Labour will continue to press the Conservative-led Government to roll out the scheme as fast as possible. The delay to date has not been fair to the innocent victims or their families."
Mr McClymont, Shadow Pensions Minister, stressed the need to bring forward the scheme to cover those affected by any future terrorist attacks.