This will be the first time that Italy serves as hosts of the Games since the 2006 Turin Winter Olympics.
Still, a big plus for the Italian bid - uniting Milan, the Alpine ski resort of Cortina d'Ampezzo, and several towns in between - was the IOC's own polling.
Sweden, a winter sports powerhouse, hosted the summer Games in 1912 but has never staged the winter Olympics.
The vote to choose a victor from the Swedish and Italian rivals is expected to be closer than the 2015 vote when Beijing beat the Kazakh city Almaty to land the 2022 Winter Games.
"We have budget problems in Italy, but I think that this is something that everyone has", Italian Undersecretary of State Giancarlo Giorgetti said at an earlier news conference, citing the wealth of the Lombardy and Veneto provinces underwriting the cost of the Games.
"We have 83 percent support across Italy for the Games and 87 percent in Milan".
The recent IOC Evaluation Commission report had appeared to give Milan-Cortina the edge, with concerns expressed over the funding for new venues in the Swedish bid - including the Stockholm Olympic Village and the speed skating oval as well as legacy use. Long term, the ice arena would be used as a multi-sport arena, National Olympic Committee of Italy President Giovanni Malago told UPI before Monday's election.
Michela Moioli, Olympic snowboard champion in 2018, added: "The whole country believes in us; it's your turn to believe in us".
Lindberg challenged her colleagues to reward a new kind of creative, cost-effective bid the International Olympic Committee has said it wanted - "Or is it just talk?"
The IOC has relaxed previously strict rules that demanded financial guarantees and government support earlier in the bidding process.
"To a person, everyone we have met today - public officials, civil servants, philanthropic leaders, citizens of the community, athletes who call this place home - everyone one of them has said to us, 'We're ready, we're willing, we're able".
Paris, France, will host the 2024 Summer Games, while the Olympics will return to the U.S.in 2028, with the action centered around Los Angeles. Salt Lake had expected to spend $10 million bidding for a future Winter Games.
During the traditionally slick and emotional pleas to be awarded the games, Stockholm mayor Anna Konig Jerlmyr reminded voters of Sweden's most famous music act.