The previous smallest country to have reached the finals was Trinidad & Tobago in 2006, with 1.3 million people.
Iceland got through to the quarter-final stage before their fairytale run was ended by hosts and beaten finalists France 5-2.
The Irish are looking to qualify for the World Cup for a fourth time, and first since 2002.
Iceland coach Heimir Hallgrimsson has expressed his disbelief after his nation secured their place at next year's World Cup.
Antonio Candreva lifted Italy to a 1-0 win over Albania in their final World Cup qualifying game that assures the Azzurri are top seeds for November's play-offs.
Sigurdsson also set up the second for Johann Gudmundsson midway through the second half as Iceland completed the campaign by winning their final three games without conceding a goal.
The win for the Egyptians, which sparked wild scenes of celebration in Alexandria and in capital city Cairo, saw them finish top of their six-team group in the African qualifying section.
"And what's more we are in a group contested between Croatia, Turkey, Ukraine and Finland, who are much better than their position in the group would have you believe".
The party analogy returned last night as Hallgrimsson and his players basked in the remarkable feat of having become the least populous nation ever to reach a World Cup.
Lagerback laid foundations for a European dream which first started with a second place in a Euro 2016 qualifying group behind Czech Republic which saw Iceland grab their first-ever participation at a major global tournament.
Iceland's players celebrate after scoring against Kosovo.