Sweden, who reached the World Cup quarter-finals last year, triumphed 2-0 away to Romania in Bucharest to seal their spot.
Marcus Berg and Robin Quaison netted first-half goals to clinch the victory and second spot in Group F behind Spain.
Romania remain third in the group alongside Norway but both are four points behind the Swedish and could only qualify via the UEFA Nations League.
Finland secured their maiden appearance at the continental championship with a 3-0 win over minnows Liechtenstein in Helsinki.
Norwich City striker Teemu Pukki was the hero with a brace, after Jasse Tuominen had opened the scoring in the first half.
Finland is certain of second spot in Group J behind Italy who maintained their perfect record with a 3-0 win away to Bosnia-Herzegovina.
Bosnia can still qualify for the Euros via the UEFA Nations League despite sitting fifth in the group.
Greece defeated Armenia 1-0 on Friday but appear unlikely to qualify for the Euros given their position in the Nations League, despite being third in the group.
Group D will come down the final day of matches on Monday, with Denmark’s 6-0 win over Gibraltar putting them clear in top, one point ahead of Switzerland who defeated Georgia 1-0.
Third-placed Republic of Ireland, who are three points behind Denmark in third, host the Danish in Dublin on Monday, while second-placed Switzerland can seal qualification by winning away to Gibraltar on Monday.