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.
"It could have been a little better, for sure." Italy coach Roberto Mancini told RAI2. "We are confident and positive, especially in the more difficult moments.
"As we would have gladly avoided them (Portugal), probably they too would have avoided us. We will have to play a great match (against North Macedonia), then we will see in the final."
Failure to advance would be a major blow for four-times World Cup winners Italy, who did not reach the 2018 edition -- the first time they missed out on qualification in 60 years.
Wales, who are looking to make their first World Cup in 64 years, were drawn in the same path as Scotland, who have not qualified since 1998.
"We've given ourselves a great opportunity. We've worked ever so hard to finish second and get that home draw. We've got everything to play for," Wales manager Robert Page told the BBC.
Older Wales fans still get high blood pressure thinking about the 1977 World Cup qualifier with Scotland.
Played at Liverpool's Anfield stadium, the Scots took the lead with a penalty awarded for handball even though replays showed it was Scotland striker Joe Jordan who handled.
Scotland won 2-0 to earn a place at the World Cup in Argentina the following year.
Eight years later, Scotland earned a vital draw in Cardiff to book a place at Mexico '86, but the celebrations were cut short after manager Jock Stein suffered a heart-attack on the touchline and died in the changing rooms shortly afterwards.
The playoff semi-finals and finals will be played from March 24-29.
FIFA also held the draw for the intercontinental playoffs where the Asian qualifier will play a team from South America while one from the CONCACAF region faces Oceania's qualifier.
EUROPEAN PLAYOFF DRAW (HOME SIDE FIRST)
Semi-final 1: Scotland v Ukraine
Semi-final 2: Wales v Austria
Semi-final 3: Russia v Poland
Semi-final 4: Sweden v Czech Republic
Semi-final 5: Italy v North Macedonia
Semi-final 6: Portugal v Turkey
INTERCONTINENTAL PLAYOFF DRAW
AFC team v CONMEBOL team
CONCACAF team v OFC team