The three countries have cleared the first hurdle to joining the European Union, leaving just Norway to settle terms, but all must now win the support of the European Parliament and their own voters.
Swedish Prime Minister Carl Bildt said the accord was his country's most important international negotiation this century.
"In substance and detail this is a very good deal," Bildt said in a statement. "In all essential matters, the EU countries have taken into account and met our viewpoints."
Finland's External Relations Minister Pertti Salolainen said: "I think that we feel quite good. One can even say that we feel happy."
Austria also noted the significance. "For us it is a very important step, one that can scarcely be exaggerated in its importance," Austrian Chancellor Franz Vranitzky said, welcoming the accord after five days of intense negotiating that culminated in a 36-hour marathon session.
Talks next Tuesday on the key issue of fishing rights will determine Norway's application.
The applicant countries will then need to win the approval of the majority of the EU's 518 European Parliament members who can block the deals.
In this task they run straight into party politics with European Parliament elections in June and those members of the assembly who are hoping to return to the new, enlarged, body already tuning their antennae towards their national electorates.
The timetable is tight. Parliament, which is not renowned for its alacrity, has just two months to vet and vote on the accords before its members hit the campaign trail.
Once that is done each accord must clear the final hurdle of a referendum in each of the applicant countries -- and the outcome is far from assured.
Opinion polls in Finland show 39 percent in favor of EU membership and 30 percent against. Around 31 per cent are undecided.
In Sweden, 42 percent of voters are opposed to EU membership and 35 percent in favor, with 23 percent undecided.
Austrians will get an opportunity to vote on the membership package in a June referendum.
If the European Parliament does approve the deals and the national referenda give the final stamp of approval, each of the applicants should be set to join the EU on the target date of Jan. 1 next year.
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