Republic of Ireland will take on Denmark while Northern Ireland face Switzerland for a place in the 2018 Fifa World Cup. Elsewhere in Tuesday's (17 October) play-off draw, Sweden were drawn against four-time world champions Italy while Croatia will take on Greece.
Martin O'Neill's side will travel to Copenhagen for the first leg of their tie before welcoming the Danes to the Aviva Stadium for the return leg. Northern Ireland meanwhile host Switzerland at Windsor Park for the first leg.
First leg ties will take place between 9 and 11 November with the second to follow between 12 and 14 November.
Martin O'Neill's side took a commanding lead in their qualifying campaign after taking 10 points from a possible 12 in their first four matches but a wretched run-in saw them needing a minor miracle in their final group game against Wales.
The Boys in Green travelled to Cardiff on Monday 9 October knowing only a victory in the Welsh capital would see them qualify for the play-off stages. A second-half strike from West Brom's James McClean sealed a famous win which keeps Irish hopes of qualifying for a first World Cup since 2002 alive.
Northern Ireland also endured a dramatic conclusion to their group, qualifying for the play-off round behind group winners Germany despite losing their final match to Norway. Their qualification was sealed ahead of kick-off thanks to Scotland's draw with Slovakia.
Michael O'Neill's side are aiming to reach their first World Cup since 1986. In Switzerland, they have been paired against the highest-ranked side in the current Fifa standings.
The Republic have secured a slightly more favourable draw and will be boosted by their recent success in play-offs. Twice they have overcome one final hurdle in recent years to qualify for major international competition, getting past Estonia in 2011 and Bosnia-Herzegovina in 2015 to reach the last two European Championships.
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 winner.