The lower house of parliament, which is controlled by Tusk's pro-EU alliance, had earlier Monday rejected the conservative camp's proposed new cabinet.
"It's a great day for everyone who over these long years firmly believed that things would get better, that we would chase away the darkness," Tusk said in parliament after 248 MPs voted in favour of him and 201 against.
"Starting tomorrow we will be able to right all of the wrongs so that everyone can feel at home in Poland," added the veteran politician, who was previously prime minister from 2007 to 2014.
His arch nemesis Jaroslaw Kaczynski, the head of the right-wing Law and Justice (PiS), fired back by accusing Tusk of being a "German agent", a claim he has made repeatedly.
European Commission President Ursula von der Leyen sent her congratulations to Tusk on X.
"Your experience and strong commitment to our European values will be precious in forging a stronger Europe, for the benefit of the Polish people," she said.
The conservatives had won the most seats in October's general election but found themselves without viable coalition partners.
In a confidence vote Monday, only 190 lawmakers voted for the right-wing government of Mateusz Morawiecki, with 266 against.
While Tusk's Civic Coalition political group came second in the election, it secured a majority by joining up with two smaller pro-EU opposition political groups, the Third Way and Left.
The trio had run on pledges to mend strained ties with the European Union and carry out liberal reforms.
Tusk on Tuesday is due to present his programme to MPs who will then hold a confidence vote.
The Tusk cabinet could be sworn in on Wednesday, allowing him to travel to Brussels for an EU summit on Thursday and Friday as the new prime minister.
Tusk has promised to unblock billions of euros in EU aid that have been frozen because of long-standing tensions between Brussels and the outgoing government.
Tusk has also said he will restore Poland's credibility in the EU and give it an important voice amid the ongoing war in neighbouring Ukraine. Ukrainian president Volodymyr Zelenskyy welcomed Tusk's election, calling on his to maintain unity between Kyiv and Warsaw.
"Ukraine and Poland's future lies in unity, mutual assistance and strategic partnership in order to defeat our common enemy," he posted on X.
"I am certain that Ukraine and Poland will reemain committed to the cause of defending global freedom."
Expectations for the new government are running high but the populists will remain very influential and have appointed allies to key posts during their time in power.
The next government will face daily battles with PiS which "will continue to fight", Jaroslaw Kuisz, a political analyst, told AFP. "There won't be any miracles."
"It will be like going through mud" and quick change will be difficult because PiS has left "a judicial minefield", he said.
Controversial judicial reforms and appointments, which the EU said undermined democratic values, were at the heart of tensions between PiS ministers and Brussels.
PiS still has allies in the presidency, the central bank and the supreme court, as well as in several important judicial and financial state institutions.
It also dominates state media organisations, which became government mouthpieces during its rule.
Analysts speak of a "spider's web" woven by PiS by putting allies in influential roles with mandates that will last long into the new government's tenure.
Polish President Andrzej Duda, an ally of the outgoing government, is due to step down ahead of a presidential election in 2025 but could use blocking tactics between now and then, vetoing legislation.
The head of state gave an insight into his intentions by nominating Morawiecki to try to form a government, giving PiS two more months in power.
Analyst Kuisz said the party has used the time "to reinforce itself institutionally and financially".
PiS has named two former ministers to head up important state financial institutions and selected new prosecutors.
The president has also approved 150 new judges nominated by a body that was criticised by the European Union as being too heavily influenced by PiS.