Tusk resigned after being picked recently as the next president of the European Council, a role that will make him a major representative for the European Union.
President Bronislaw Komorowski presented Tusk with a seafarer's compass for his "long journey" to Brussels, saying "with a good compass you can always find your home port and safe harbor."
Komorowski noted that it was unprecedented for Poland to hold such a leading role at the EU and called it a source of pride for all of Poland.
Tusk is to be succeeded by Ewa Kopacz, the 57-year-old parliament speaker and a former health minister and pediatrician. She is a member of Tusk's center-right Civic Platform party and is said to have been picked by Tusk as his successor for her loyalty to him.
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It is not yet clear if key ministers, including Foreign Minister Radek Sikorski, will continue in their roles under Kopacz, though at least a few ministers are expected to be replaced.
Some political observers are calling for as much continuity as possible, arguing that stability is important, given the crisis nearby in Ukraine.
Kopacz has said she hopes the vote will take place September 26. She would almost certainly win the parliament's support since Civic Platform and its junior partner, the Polish People's Party, hold a majority.
She is to become Poland's second female prime minister after Hanna Suchocka, who served in the early 1990s.
The new government will only have a year in office before elections are held in 2015.