The 12 teams -10 of which finished runners-up in their groups - were split into three four-team paths, each with its own semi-finals and final. Seeded teams were guaranteed a home game in the semi-finals.
The winning team from each path qualifies for the World Cup in Qatar, meaning Italy and Portugal cannot both reach the tournament.
Italy, who won the Euros earlier this year, and 2016 European champions Portugal will play their semi-final games at home against North Macedonia and Turkey, respectively.
Should the two heavyweights advance, Portugal will have home advantage in the final.
Failure to advance would be a major blow for four-times World Cup winners Italy, who did not qualify for the 2018 edition - the first time they missed out on qualification in 60 years.
Wales, who are looking to reach their first World Cup in 64 years, were drawn in the same path as Scotland, who have not qualified since 1998.
The semi-finals and finals will be played from March 24-29.