Aiming to reach its first major finals in 22 years, Steve Clarke's side will face Israel in a one-legged tie at Hampden Park on 27 March (AEDT).
The winner of that match will go on to face either Norway or Serbia in the Path C final five days later.
Scotland beat Israel 3-2 at Hampden Park last November en route to topping their UEFA Nations League group and Clarke is after a repeat result in four months' time.
"The draw is what it is," he said. "I never get too carried away about who you are going to play.
"It would been nice to repeat the home win, but the match will come with its own level of pressure, which we will have to embrace.
"Being at home is very important for us. I'm sure Hampden will be full, with the Tartan Army on the march. It's a great stadium when it's full, so if we start fast we can get them all behind us."
Northern Ireland and Republic of Ireland are on course to meet in the Path B final, having been drawn away to Bosnia and Herzegovina and Slovakia respectively in the semi-finals.
In Path A, Romania will travel to Iceland and Bulgaria will host Hungary, while Belarus will be at Georgia and North Macedonia at Kosovo in Path D.
The four play-off winners will join the 20 teams that have already qualified for the finals, which will take place in 12 different European cities next year.