Slovak Prime Minister Robert Fico says the countries take the bid "extremely seriously" and will do all they can to make it successful.
Under the proposal, the hub would be Poland's historic city of Krakow, with most snow events in the Tatra mountain resorts of Zakopane. Jasna would host Alpine skiing in Slovakia.
Zakopane and the Slovak resort of Poprad have failed in previous separate bids.
Polish Prime Minster Donald Tusk says after meeting Fico in Poprad that a joint bid has "an extraordinary chance" to succeed.
The IOC will choose a host city in 2015.