Israel's failure to beat Cyprus means Chris Coleman's side will play at next summer's tournament in France.
Milan Duric scored a looping header before Vedad Ibisevic added a tap-in.
Wales last played at an international tournament in the 1958 World Cup, and had never before qualified for the European Championship.
Wales join Northern Ireland and England in France next year. The Republic of Ireland can still qualify if they either beat Poland in Warsaw on Sunday or draw a higher score than 1-1.