Defence Secretary Des Browne said he would be seeking a group pardon, approved by Parliament, for the men.
It is thought 306 British soldiers were shot for cowardice, desertion or other offences in the 1914-1918 war.
Among them was Private Harry Farr, shot for cowardice in 1916 aged 25. His family said they were "overwhelmed".
They have been campaigning for years for him to be pardoned, arguing that he was suffering from shell-shock and should not have been sent back to the trenches.
Mr Browne told BBC Radio 4's Today programme that, after 90 years, "the evidence just doesn't exist inside the cases individually".
"I don't want to be in a position of second guessing the commanders in the field who were making decisions," he added.
But injustices "were clearly done".
"We can't be in a situation morally where we cannot redress injustices because we don't have paperwork in relation to an individual case.
"But we can in other cases where we have some paperwork."
A statutory "blanket pardon" recognised that the men should not have been executed, Mr Browne said.
"But it also recognises that everybody involved in these terrible cases were as much victims of World War I as those who died in the battlefield."
But Gary Sheffield, professor of modern history at King's College London, told Today the decision raised "some very difficult issues" about how historical evidence was used.
He said that when the government had previously considered the issue in 1998 it had decided against a blanket pardon.
The reason given was because it said it could not "distinguish between those who deliberately let down their country and their comrades and those who were not guilty of desertion of cowardice", he said.
"That struck me as being true in 1998 and equally true today," Mr Sheffield added.
I'm not sure how I feel about this. On the one hand it is very hard not to feel sympathetic for Parr and the situation he was in and I'm not against issuing pardons if an injustice was done; but on the other I'm against re-writing history to suit current mores and preferences.
As pointed out in the article back in 1998 the government decided against a blanket pardon due to lack of evidence; and now for the same reason they are issuing a blanket pardon? Most of those executed were guilty and dealt with by the law *as it stood at the time* (including 37 murderers). Personally this looks like Labour trying to get some "feel good" news in the papers without actually doing anything. I'd be far more impressed if they did something for the many living veterans that could do with help and to which the government could do more than make meaningless gestures.