The Swedish Olympic Committee delivered the bid to the International Olympic Committee, three days before the deadline.
Stockholm hosted the 1912 Summer Olympics, as well as the equestrian competition of the1952 Melbourne Games.
Stockholm joins another Scandinavian capital — Oslo, Norway — in the 2022 race.
The Swedish committee said the games would be an urban event, with the majority of sports hosted in the capital. Four Alpine ski competitions — downhill, giant slalom, super G and the combined — would be held in Are, 650 kilometres (400 miles) north of Stockholm.
A review of the conditions to host the games concluded that existing venues have enough capacity to hold most events. One of the biggest planned investments would be to raise the height of an existing ski slope in Stockholm by 100 metres (330 feet) to meet the criteria to host the slalom competition.
"We could give the world an exciting and original project that would be both spectacular and brings winter sports into the city in a unique way," the Swedish committee said in a statement.
The committee will continue to investigate the financial and technical conditions and submit a final application to the IOC on March 14.
Six candidates are now in the running for the 2022 Games. In addition to Stockholm and Oslo, they are: Lviv, Ukraine; Beijing and the northern Chinese city of Zhangjiakou; Almaty, Kazakhstan; and a joint bid from Krakow, Poland, and Jasna, Slovakia.
On Sunday, voters in Germany rejected plans for Munich to bid for the games. Opponents were concerned about environmental issues and high costs.
In March, another potential European favourite was rejected in a referendum. Switzerland dropped its candidacy from St. Moritz, the 1928 and '48 host, when voters in the region refused to support it amid concerns over cost and disruption.
The IOC will select the 2022 host city in 2015.