The play-off draw determines that one of the most high-profile players will be involved in the Euro play-offs at 2014 World Cup in Brazil.
Sweden pips Portugal in their head-to-head record; the teams have met 15 times, with the Scandinavians winning six, drawing six and losing three.
France will face Euro 2012 co-hosts Ukraine, who have not lost in 11 matches.
Euro 2004 winners Greece will take on Romania, while Iceland face Croatia in their bid to become the smallest nation at the World Cup.
The first legs will be played on November 15, with the returns on 19.