"Today I am the happiest person in the world," a teary-eyed Tusk told supporters. "People in Poland voted today to choose their own fate and have put a great responsibility, a great task on our shoulders. We undertake this great responsibility."
Kaczynski conceded defeat late last night, saying, "we didn't manage in the face of this unprecedented broad front of attacks," referring to the opposition's campaign.
His Law and Justice party got 32.6 percent of the vote, or 173 seats, according to partial results. Complete results are expected either later today or tomorrow.
Kaczynski said a coalition with the election winner was "out of the question" and pledged to use his time in the opposition to rebuild his forces - and keep a close check on the new government.
A hard-fought campaign generated voter turnout of 52.6 percent, higher than any parliamentary elections since the fall of communism in 1989, according to an exit survey conducted by the PBS DGA polling institute. The high turnout caused some polling stations to run out of ballots and stay open longer than scheduled, delaying the release of the first exit polls for hours.
The election result means Poland will no longer have twin brothers holding the two highest offices; Jaroslaw Kaczynski will remain the country's president with a term lasting until 2010. The 58-year-olds are former child movie stars who as adults became activists with the Solidarity trade union movement that helped topple communism in 1989.
Both Tusk and Kaczynski favor good relations with the United States, but Tusk argues Poland has not gotten enough from its close ties with Washington and wants the country's 900-strong detachment in Iraq to come home. He also says Poland should drive a tough bargain in return for hosting a missile defense base.
The 50-year-old Tusk, the favorite to become the next prime minister, said the election showed that Poles want to focus on the economic opportunities presented by the country's membership in the EU, which Poland joined in 2004.
"It is Civic Platform's intention to make Poles feel much better in their own country than they have felt so far," Tusk said. "You have the right to rejoice today."