Tusk, 50, replaces the president's twin brother as premier. Jaroslaw Kaczynski's conservative, nationalist government was forced to call elections two years early after his ruling coalition collapsed.
Tusk leads a coalition of his Civic Platform Party and the centrist Polish People's Party. The two parties together have 240 seats in parliament, giving them more than the 231 votes needed to approve a government.
Waldemar Pawlak, who leads the Polish People's Party, has been appointed deputy prime minister and economics minister. Of the 17 ministers in the new cabinet, five are women.
Tusk earlier said that he was ready to cooperate with his political rival, the president, on all key issues. Tusk unsuccessfully ran against Lech Kaczynski in the 2005 presidential elections, and Kaczynski has openly voiced his doubts over the new premier.
The prime minister earlier said his government would make maximum efforts to improve relations with Russia, which have been consistently frosty since the fall of communism in Europe. He is also expected to seek closer ties with Germany and the rest of the European Union.
Tusk is set to deliver a speech in parliament on November 23, after which lawmakers will hold a vote of confidence on the new coalition government.