The Housing Secretary, James Brokenshire, put forward the new plans for consultation in order to ensure that ex-service personnel with mental health issues get the same treatment as those with physical injuries.
The proposed changes will also make it easier for the partners of armed forces personnel to get social housing, even if they have divorced or separated from their partners.
Brokenshire said: "We have a duty to ensure military personnel get the support they need.
"We want to see that applying for social property should not be a challenge in the transition to civilian life.
"These new measures are part of our continuing commitment to the Armed Forces Covenant."
Under the current rules, partners who separate from service people must move out of their military accommodation, and can often then struggle to find social housing because they 'have not been resident in the area for long enough'.
In addition to this, there are circumstances in which the partner may not want to remain in the area - for example, if they have been a victim of domestic abuse.
Certain councils already have protocols in place to support ex-military personnel but these proposals are aiming to encourage all councils to waive residency rules.
These new proposed measures follow on from protections that were introduced in 2012 to ensure that there could be no discrimination to military personnel as a result of them moving from place to place due to their work.
This included a change in the law that meant that all seriously injured and disabled service personnel, as well as other former members of the armed forces, are given high priority when it comes to social housing.
This is part of the government's ongoing plan to create 250,000 homes - including some social housing - by March 2022. The plan will see £9 billion ($11.5bn) in funds applied to creating affordable housing.
The new rules are now subject to an eight week consultation period.
Ray Lock, CEO of the Forces in Mind Trust - an armed forces mental health charity - said: "Well over 1,000 men and women leaving the Armed Forces need urgent support to find accommodation every year. Our research has shown that the advice given to veterans can be patchy.
"We welcome these proposals, which will undoubtedly make a significant difference to those in most need.
"But we urge ministers to also ensure veterans feature in local authority housing strategies and appropriate advice is given to anyone applying for housing advice who is identified as a veteran.
"That is the single most important step towards ending homelessness among those who have served our country."