The Dark Blues are due to face Temuri Ketsbaia's side on Saturday, October 11.
Hampden is out of commission after being converted into an athletics venue for next month's Commonwealth Games in Glasgow.
That means Gordon Strachan's side will instead play their first home match of the Euros qualifying campaign at Rangers' 51,000-seater arena.
It will be the 18th time the ground has hosted a full Scotland international, and the first since Craig Brown's team beat Bosnia-Herzegovina 1-0 in October 1999.
The SFA say they will also announce the venue for November's qualifier against Republic of Ireland shortly, with Celtic Park expected to be given the nod.
Scotland will kick-off their bid to reach the finals in France with a trip to Germany's Westfalenstadion in Dortmund.