Twelve teams entered the play-offs based on their performance in the 2022-23 Nations League. That was whittled down to six after Thursday's semi-finals.
Standing between Wales and a place at the Euros is Poland, who thrashed Estonia 5-1 in their semi-final.
Iceland fell behind early on against Israel but came back to win 4-1 and set up a meeting with Ukraine, who scored two late goals to stun Bosnia and Herzegovina 2-1.
That game will be held in the Polish city of Wroclaw with Ukraine unable to host it because of the continuing invasion by Russia.
Georgia, who have never qualified for a tournament, beat Luxembourg 2-0 and will now play 2004 European champions Greece, who breezed past Kazakhstan 5-0.
Tuesday's play-off final fixtures (kick-off 19:45 GMT unless stated):
Path A: Wales v Poland
Path B: Ukraine v Iceland
Path C: Georgia v Greece (17:00 GMT)
What are the groups for Euro 2024?
Group A: Germany, Scotland, Hungary, Switzerland
Group B: Spain, Croatia, Italy, Albania
Group C: Slovenia, Denmark, Serbia, England
Group D: Play-off winner A, Netherlands, Austria, France
Group E: Belgium, Slovakia, Romania, Play-off winner B
Group F: Turkey, Play-off winner C, Portugal, Czech Republic
Play-off winner A: Poland or Wales
Play-off winner B: Ukraine or Iceland
Play-off winner C: Georgia or Greece