Scotland and Wales will meet each other in a World Cup play-off final if they win their respective semi-finals.
Wales will play Austria at home in their play-off semi-final.
Scotland were drawn in the same play-off path as Wales and will have home advantage against Ukraine in their semi-final on March 24.
The winners of the Wales-Austria game will host the final against either Scotland or Ukraine.
Wales manager Robert Page believes his side have a “great opportunity” to reach the World Cup finals in Qatar next year.
“We’ve given ourselves a great opportunity,” Page told BBC Sport after the draw.
“We’ve worked ever so hard to finish second and get that home draw. We’ve got everything to play for.”
Scotland manager Steve Clarke expected a difficult semi-final no matter which of the six possible opponents came out of the hat.
“It will be a tough game,” Clarke said. “I don’t think it matters who we were going to get in the semi-final draw, it was always going to be tough.
“We will go away and do our homework on Ukraine and try and come up with a winning formula.”
Clarke rebuffed suggestions a potential derby clash with Wales could be a distraction ahead of the Ukraine game.
“We certainly won’t be distracted by it,” he said. “We always treat our immediate opponents with the utmost respect.
“Over the winter months we will obviously have to prepare for either Wales or Austria and we’ll make sure we are well prepared for that if we manage to get through the first game.”
European champions Italy were drawn against North Macedonia, the lowest ranked team in the play-offs with a world ranking of 67.
Italy, who failed to qualify for the 2018 World Cup, will have home advantage for that tie and would meet Portugal or Turkey in a potential heavyweight final clash.
Russia will be at home to Poland in their play-off semi-final with the winners playing Sweden or the Czech Republic in another final.