The Court of Appeal ruled in October that soldiers' relatives could claim for damages for negligence, but appeal judges said that they could not make damages claims under human rights legislation.
Relatives' lawyers took the fight to the Supreme Court, which will analyse the issue next year.
The appeal will be heard in the week of Monday February 18 and the hearing is expected to last up to three days.
Seven justices will hear the appeal. Judgment is expected to be reserved.
More top news
MSPs voted 69 to 59 to mandate the First Minister to seek permission from the UK Government for a ballot to be held.
Expectant mother was mown down in the street as she tried to stop attempted fraudsters making a getaway.
A father has been found guilty of murdering his three-month-old son by hurling him "vigorously" against a hard surface in a fit of temper.