Lawyers for the family members, who can now proceed to trial, said the ruling means the Ministry of Defence owes a duty of care to properly equip service personnel who go to war.
Debi Allbutt, who had brought one of the claims over the death of her 35-year-old husband Stephen in March 2003, said she "jumped up and down with joy" when she heard the news.
"We've proven they (the government) owe a duty of care, and they can no longer hide behind the idea of combat immunity -- the soldiers have a right to life under human rights law," she said.
However, Defence Secretary Philip Hammond said he was "very concerned at the wider implications of this judgment".
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It "could ultimately make it more difficult for our troops to carry out operations and potentially throws open a wide range of military decisions to the uncertainty of litigation", he said.
The case concerns three sets of claims arising from the deaths and injuries of British soldiers serving in Iraq between 2003 and 2006.
Her husband and another soldier were killed and Twiddy and Julien were injured when their Challenger 2 tank was hit by another.
The claimants argued that the soldiers were not trained sufficiently and the tanks lacked the technology and equipment that would have prevented the incident.
The Ministry of Defence (MoD) had argued for the claims to be struck out on the principle of combat immunity, which excludes liability for negligence for those involved in active service.
But the Supreme Court judges rejected this in a majority verdict.
Another set of claims was brought by relatives of Phillip Hewett, 21, and Lee Ellis, 23, who were killed in two separate incidents in 2005 and 2006 when their lightly armoured Snatch Land Rovers hit roadside bombs.