During his trial, Blackman, who denied murder, said he believed the victim was already dead and he was taking out his anger on a corpse.
Speaking on BBC Radio 4's Today programme, Claire Blackman said: "We are just waiting for the [release] date to be calculated but know it will be fairly imminent".
Jonathan Goldberg QC told the panel of judges, headed by Lord Chief Justice Lord Thomas, that Blackman was the "last casualty of a failed war".
Following a campaign led by his wife, the conviction was quashed after the court martial appeal heard he had been suffering from a mental disorder at the time of the shooting in Helmand in 2011.
The judges said that Blackman had been "an exemplary soldier before his deployment to Afghanistan in March 2011", but had "suffered from quite exceptional stressors" during that deployment.
According to The Times, his wife Claire Blackman has now revealed the pair has received advice on upgrading security at their home, alerting police to their whereabouts, minimising their online presence, and on what to do if they are followed.
On Tuesday, Blackman spoke out about his sentence being reduced from ten to seven years, which effectively assures that he will be freed in the near future.
The judges also concluded that Blackman should be dismissed from the service, but not with disgrace.
She added: "We would of course like to thank our fantastic legal team for their excellent work".
Blackman, who watched Tuesday's proceedings by video link, has already spent nearly three and a half years in prison following his original conviction in November 2013.
When Blackman's murder conviction was overturned, his lawyer told talkRADIO that the soldier had reached "breaking point" due to his experiences in Afghanistan, and this pushed him to shoot the injured militant.
Footage from another marine's helmet camera showed Blackman shooting the militant in the chest at close range, then saying: "Obviously this doesn't go anywhere, fellas". Shuffle off this mortal coil, you c***. Several marines are killed, including Sgt Blackman's troop commander, and others are maimed.
Veterans hugged, cheered and waved flags bearing former Royal Marine Alexander Blackman's image outside the Royal Courts of Justice in London after the ruling, which means he could be released within weeks.
Windows update will bring 3-D, game tools and less clutter
Before, to share live streaming of game play, gamers had to install and activate Beam or a competing service separately. Setting tabs aside is meant to be used for pages that users don't want to bookmark, but don't need immediate access to.