Ireland, whose only appearance at a European Championship came back in 1988, were given a huge boost in their bid to reach next year's finals when they were drawn to play Estonia in the two-legged playoffs on Thursday.
The other three matches pitted Turkey against Croatia, the Czech Republic against Montenegro and Bosnia against Portugal.
The ties will be played on November 11/12 and November15.
The four winners will advance to next year's finals being staged in Poland and Ukraine.
Ireland, who controversially missed out on last year's World Cup finals after losing a playoff when Thierry Henry handled the ball in the build-up to France's winner, start as the strong favourites to progress this time.
Estonia, traditionally one of Europe's weaker nations, exceeded expectations by finishing second in their group, and would cause a major upset if they beat Ireland over two legs.
Turkey v Croatia is a repeat of their epic Euro 2008 quarter-final clash in Vienna, when Croatia went 1-0 up in the last minute of extra time, only for the Turks to equalise with the last kick of the game.
The Croatians then missed three penalties in the shootout while Turkey scored theirs and advanced to the semi-finals.
Bosnia v Portugal will be a repeat of the 2010 World Cup playoffs, when the Portuguese won 2-0 on aggregate to go through to the finals in South Africa.