Deputies of the lower house (Sejm) voted 238 to 204, with two abstentions, to support the new cabinet.
In a three-hour speech to the legislature on Friday, Donald Tusk outlined his government's policy priorities, touching on tax cuts, adopting the euro, and withdrawing troops from Iraq.
On ties with Moscow, Tusk said: "Absence of dialogue does not serve the interests of either Poland or Russia. It harms the reputations of both countries."
Relations between the countries, which have been consistently frosty since the fall of communism in Europe, hit new lows under Tusk's predecessor Jaroslaw Kaczynski, the twin brother of right-wing conservative President Lech Kaczynski.
Russia's two-year ban on Polish meat exports has proved a key stumbling block in bilateral relations, and prompted Warsaw to veto talks on a new cooperation pact between the European Union and Russia. However, since Tusk's victory in last month's elections, Warsaw has shown willingness to accommodate Russia's demands on the issue.
Earlier in the month Poland invited Russian experts to inspect Polish meat factories to pave the way for a lifting of the ban, which was imposed over accusations that Poland was supplying poor-quality meat from third countries. On Thursday, Poland's agriculture minister reiterated that Warsaw is ready to negotiate.
On the controversial issue of Poland's involvement in Iraq military operations, the prime minister said that his government would ensure a complete withdrawal of troops by the end of next year, in line with his Civic Platform party's pre-election pledge.
"In one year's time, I will announce to you here in this chamber that our military mission in Iraq is over," Tusk said. "Poles have been anticipating this decision," he added.
However, President Lech Kaczynski, a staunch ally of Washington who fully supported the 2003 invasion of Iraq, has yet to approve the government's decision on a pullout. About 900 Polish servicemen are currently serving in the south of war-torn Iraq.
The prime minister stressed that the process of withdrawing Polish servicemen would be coordinated with its allies, primarily the United States.
