Tuesday's win over Armenia ensured Giovanni Trapattoni's men finished second in Group B and they were paired off with the Group C runners-up in this afternoon's draw. Estonia have never reached the finals of a major tournament, and this is Tarmo Ruutli's side's first play-off appearance.
The first leg will take place in Estonia on either 11 or 12 November, with the return leg at Dublin's Aviva Stadium on 15 November. Estonia finished ten points behind group winners Italy in qualifying, with six of their points coming courtesy of wins over Northern Ireland.
The Republic emerged from a tough group containing winners Russia and the likes of Armenia and Slovakia to secure second spot by four points. They have only reached the European Championship finals once before, in West Germany in 1988.
The other fixtures drawn today see Turkey meeting Croatia, Czech Republic taking on Montenegro, and Bosnia-Herzegovina going up against Portugal. The Portuguese and Bosnia were both beaten in winner-takes-all showdowns on Tuesday, with Portugal losing to Denmark and surrendering top spot in Group H.
Bosnia drew 1-1 with France when a win would have seen them pip Laurent Blanc's men to the automatic spot in Group D. The Czechs took second in Group I, winning a two-way tussle with Scotland to finish behind reigning champions Spain.
Former Republic of Ireland striker John Aldridge has backed the team to beat Estonia and qualify for the finals. Asked if he thought Trapattoni's side would go through, he told Sky Sports News: "Yes. We've got the greatest travelling fans and it would be great to see them on the road again."
The former Liverpool player believes the Republic were fortunate to draw Estonia. He said: "It was probably the easiest of the four [seeded teams to draw]. We travel better than we play at home, we've had better results away than we have had at home."
Aldridge added on his hopes for the first leg: "They will try to get a clean sheet, try to get a win which would set us up nicely."
Aldridge admitted the suspension of striker Kevin Doyle, still waiting to hear the length of his punishment after being sent off in the qualifier against Armenia on Tuesday which the Republic won 2-1, would be a blow to the team's chances.
However, he backed Shane Long to fill the breach. "Shane Long has done really well when he has deputised for either Robbie [Keane] or Kevin so it's a great opportunity for him."
Ireland and Estonia have met twice before, in qualifying for the 2002 FIFA World Cup™. The Irish, then under Mick McCarthy's management, won both games 2-0, with defender Richard Dunne, a scorer against Armenia, on target in each match.
Portugal coach Paulo Bento said: "We have a strong team and now we must concentrate on beating Bosnia. It is very important for us to do so. I am confident next year we shall be playing in Poland and Ukraine."