The Ministry of Defence will remove the need for Commonwealth citizens to have lived in the UK for five years before applying for service, it will be announced on Monday.
An extra 1,350 personnel from overseas are hoped to be enlisted to the Navy, Army and Air Force every year.
Applicants from nations including India, Australia, Canada and Fiji will be considered for all roles in the forces, without having lived in the UK.
Until now, they had to have resided in Britain for five years and their recruitment was capped at a maximum of 200 per year.
The Army will begin the admissions from early next year, while the Navy and RAF will commence the process immediately.
Other than the Nepalese Gurkhas and applicants from the Republic of Ireland who can enrol under a special arrangement, those from outside the Commonwealth will still need British citizenship to apply.
In April, a National Audit Office report said the full-time military was running at a 5.7% shortfall.
An extra 8,200 regulars and 2,400 engineers were needed to fill the “largest gap in a decade”, the report added, while intelligence analysts and pilots were also in demand.
The public spending watchdog is carrying out a review of army recruitment, including the contract with outsource firm Capita.
Critics have called for Capita to be stripped of its contract over forces staffing shortfalls.
In January the Army unveiled a recruitment advertising campaign reported to have cost £1.6 million.
It intended to encourage more people from different backgrounds, genders, sexualities and faiths to join up.
However it was criticised for failing to target those most interested in joining the forces.
Colonel Richard Kemp, former commander of British forces in Afghanistan, said the main group of people considering signing up are more worried about “how they are going to face combat”.
He added: “This also reflects the fact that the Army, like the rest of Government, is being forced down a route of political correctness.
“What is most important is that the Army recruits and is full of soldiers. It’s of secondary importance that they reflect the composition of society.”