EU officials said they would now work into the evening to try to get Austria to agree to a pact.
Norway, the fourth applicant involved in marathon talks with the 12-nation bloc, had already indicated that it would postpone further high-level discussions until an EU foreign ministers meeting next week.
Swedish and Finnish acceptance of membership deals -- which must be ratified in referenda at home -- came after more than 30 hours of nonstop talks on issues ranging from agricultural subsidies to budget contributions.
"We are very happy," Sweden's chief negotiator Ulf Dinkelspiel said after his country overcame last-minute concerns and accepted an offer to join.
"In the final analysis we have a very good agreement that constitutes a very good basis for the referendum to follow," he said.
Diplomats said the deal with Finland, which had been expected somewhat earlier, came after Spain backed down from two hours of resisting Finnish demands to protect its market from an onslaught of products that included wine, processed food, vegetables and cut flowers.
One of the sticking points in Sweden's negotiations was the size and timing of net contributions to EU coffers.
The pact which clinched the political deal centered on a compensation fund of around $493 million for the country having aligned its prices for farm products with those of the union, diplomats said.
Finland's main concern throughout the negotiations has been its contribution to the bloc's budget and protection for its Arctic agriculture.
Austria also has a problem with compensation for its farmers for having to slash their prices to EU levels, but its main difficulty has been its insistence on maintaining a limit for the next 10 years on heavy lorries crossing the Alps.
Norway has had the most problems, primarily over a Spanish demand for its fishing fleet to be allowed back into Norwegian waters after a gap of 14 years.
If all four countries were to join the union -- which last added new members in 1986 with Spain and Portugal -- the bloc would grow in size by nearly a half and in wealth by about 10 percent.
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