Euro 2016 in France next summer were confirmed after the two legged play-off matches.
Hungary, the Republic of Ireland, Sweden and Ukraine will join hosts France and Albania, Austria, Belgium, Croatia, Czech Republic, England, Germany, Iceland, Italy, Northern Ireland, Poland, Portugal, Romania, Russia, Slovakia, Spain, Switzerland, Turkey, and Wales in the competition.
Sweden, who finished third in Group G came through against Scandinavian rivals Denmark, who were third in Group I. The Swedes were grateful yet again to PSG striker Zlatan Ibrahimovic, who scored three goals over the two legs.
Hungary, who finished third in Group F came through against Norway, third in Group H, behind Italy and Croatia.
The Republic of Ireland, third in Group D behind Germany and Poland, beat Bosnia & Herzegovina, third in Group B.
Euro 2012 co-hosts Ukraine, third in Group C, advanced against Slovenia, who finished third in Group E.
Friday, November 13
Norway 0 v Hungary 1
Saturday, November 14
Bosnia & Herzegovina 1 v Ireland 1
Sunday, November 15
Ukraine 2 v Slovenia 0
Sweden 2 v Denmark 1
Monday, November 16
Hungary 2 v Norway 1
Tuesday, November 16
Ireland 2 v Bosnia & Herzegovina 0
Wednesday, November 17
Denmark 2 v Sweden 2
Slovenia 1 v Ukraine 1
The draw for the final groups will be made in December.