Tusk, 50, is to receive the mandate in a brief ceremony at the Presidential Palace in downtown Warsaw.
He is the leader of the pro-business and EU-friendly Civic Platform party that in Oct. 21 elections won over the nationalist and conservative Law and Justice party of Prime Minister Jaroslaw Kaczynski, the president's twin brother.
Kaczynski's government stays on as caretaker until Tusk's Cabinet gets approval from the parliament, expected this month.
With 209 seats, Civic Platform is short of a majority in the 460-seat Sejm, or lower house of Parliament, and is concluding coalition talks with the small centrist Polish People's Party, also known as Polish Peasants' Party. They jointly have 240 seats.
Tusk, who has vowed to work to improve ties with the EU, Germany and Russia and strengthen the alliance with the United States , said he will announce his government composition next week, probably on Wednesday, when the parliament convenes.
Jan Dziedziczak, spokesman for the outgoing government, said premier Kaczynski has "cordially invited" Tusk to use an office at the premier's headquarters building for his coalition talks, that should be held in "comfortable conditions."
It was seen as a conciliatory gesture following years of bitter rivalry between the two parties that failed to form a coalition after the 2005 election, when Law and Justice narrowly won over Civic Platform.
Kaczynski then sealed a coalition with two small, unpredictable, populist parties, but the pact collapsed last summer, leaving him with a minority government and triggering elections just half way through a four-year parliament term.