It will take a monumental effort from the "Boys in Green" to secure a place at the World Cup draw on December 1 in Russian Federation as all four of Ireland's potential opponents are ranked inside the top 20 of FIFA's world rankings.
Italy are four time winners of the World Cup, having last won in 2006.
The two-legged ties are set for November 9-11 and 12-14.
The FAI have announced that Ireland fans can buy tickets to the home leg of the play-off involving Martin O'Neill's side from Friday, October 20.
Following Tuesday's draw in Zurich, Ireland avoided tricky ties against both Italy and Croatia and will travel to Copenhagen before a return leg in Dublin at the Aviva Stadium in November. Their qualification was sealed ahead of kick-off thanks to Scotland's draw with Slovakia. In Switzerland, they have been paired against the highest-ranked side in the current Federation Internationale de Football Association standings.
The Republic last reached the finals in 2002.
In 2009, they reached this same stage ahead of the 2010 World Cup where they lost out to France, a contest made famous for Thierry Henry's handball in the build-up to a French victor.