Krakow is bidding jointly with Slovakia, which would hold some of the snow events in Jasna in the Tatras mountains.
Five of the six countries have bid for the Winter Games before, with Ukraine the only newcomer.
Stockholm or Beijing would become the first city to host both the Summer and Winter Olympics.
Beijing hosted the 2008 Summer Olympics. Stockholm held the 1912 Games and the equestrian competition for the 1952 Melbourne Olympics. Oslo hosted the 1952 Winter Olympics, and the Norwegian town of Lillehammer staged the 1994 Games.
The confirmation of the bid cities marks the start of a two-year campaign that will end with the selection of the host city in July 2015.
The IOC said the field "includes a strong mix of both traditional and developing winter sports markets."
The race has twice as many candidates as the previous winter campaign, when the South Korean resort of Pyeongchang defeated Munich and Annecy, France, for the 2018 Games.
"These cities and their supporters clearly understand the benefits that hosting the games can have and the long lasting legacy that a games can bring to a region," IOC President Thomas Bach said of the 2022 bid cities.
The IOC did not mention that potential 2022 bids from two major European winter sports countries were turned down in recent referendums.
Last week, voters in Bach's home country of Germany said no to another bid from Munich, citing financial and environmental concerns. In March, Switzerland dropped plans for a bid from St. Moritz, the 1928 and '48 host, when voters in the region refused to support it amid worries over costs and disruption.
The new bidding comes amid concerns over the costs of the 2014 Winter Games in Sochi, Russia, where the overall price tag is more than $50 billion — a record for any summer or winter Olympics.
"Maybe some of the investments we have seen in Sochi with $50 billion has scared some people away," senior Norwegian IOC member Gerhard Heiberg told The Associated Press. "I felt that when Switzerland pulled out and I felt even stronger when all the four constituents in Germany said no. This needs to be taken seriously by the IOC. We have to look at this and find out what happened and why did it happen."
With that in mind, he said, the future of the Olympics could be driven by whether cities can afford to host the games.
"If the costs and investments are so high, many countries, many cities will shake their heads and say this is too much for us," Heiberg said in a telephone interview. "We have to find ways and means of saving costs and investments, otherwise we will not have any applicants for the Winter Games, and the same applies for the Summer Games."