They will be joined by holders Spain, who made no mistake in beating Georgia 2-0 at home in Albacete, and England, who also won 2-0 at home yesterday to Poland to reach their fifth successive World Cup finals.
England's manager from their failed 2010 finals campaign Fabio Capello will also be in Brazil after Russia got the point they needed with a 1-1 away draw at Azerbaijan.
It will be the 2018 World Cup hosts' first World Cup finals since 2002.
Vedad Ibisevic was Bosnia's hero as he scored what was the most important of his 20 international goals as the 29-year-old Stuttgart striker struck in the 68th minute.
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Bosnia coach Safet Susic, who appeared in two World Cup finals for the former Yugoslavia, was ecstatic.
"I congratulate these guys for their great work in the last four years," he told local TV.
"It would have been a real injustice if we had failed to win the group and qualify for the World Cup."
Greece by contrast have failed to sparkle in front of goal and were only able to beat Liechtenstein 2-0 in Athens leaving them with just 12 goals in their 10 qualifiers.