With 209 seats, the Civic Platform party is short of a majority and is in coalition talks with the Polish Peasants' Party. The two parties would together have 240 seats.
Poland held a general election on October 21, two years early, after the last coalition collapsed amid acrimony over a corruption investigation.
Tusk has pledged to improve Poland's relationship with the rest of the European Union - and with neighbouring Germany in particular - and to improve the nation's often tense relations with Russia.
He has said he will withdraw Polish troops from Iraq, where 900 soldiers are serving and is far more critical of the US's controversial plan to place part of its anti-missile system in Poland.
However, his new government may face problems implementing changes, particularly a controversial plan to instigate a flat rate of income tax, as the president could veto such plans in parliament.
The president has the right to represent Poland abroad and shares responsibility with the head of the government at EU summits and in ambassadorial appointments.