Italy were held to a 0-0 draw. The result means the Azzurri will not be present in the competition for only the second time in their history having declined to play at the inaugural tournament in 1930.
Midfielder Jakob Johansson's deflected strike in the first leg was the difference as the second leg at Milan's San Siro stadium ended goalless, BBC reported on Tuesday.
Sweden sat back on their advantage and, despite the hosts enjoying 76 per cent possession, they failed to find the breakthrough - Italy's best chance saw goalkeeper Robin Olsen palm away substitute Stephan El Shaarawy's thumping late volley.
Striker Ciro Immobile missed a number of chances and his low effort in the first half was cleared off the line by centre-back Andreas Granqvist.
The result sees Jan Andersson's Sweden side reach the World Cup for the first time since 2006, when they were in the same group as England.
A tearful Gianluigi Buffon said he was "sorry for all of Italian football" as he led a wave of international retirements after a World Cup play-off defeat by Sweden.
Buffon, 39, said: "It's a shame my last official game coincided with the failure to qualify for the World Cup.
"Blame is shared equally between everyone. There can't be scapegoats."
Buffon's Juventus team-mate Andrea Barzagli and Roma midfielder Daniele de Rossi also ended their Italy careers, while Giorgio Chiellini is expected to join them. The quartet have won 461 caps between them.
Goalkeeper Buffon made 175 appearances for his country in a 20-year career - lifting the World Cup in 2006 - and believes the future could still be bright for the four-time world champions.
"There is certainly a future for Italian football because we have pride, ability, determination and after bad tumbles, we always find a way to get back on our feet," he said.
Italy manager Giampiero Ventura -- under contract until 2020 -- did not speak to national television after the defeat but arrived at a news conference 90 minutes after full time.
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