With about 95 percent of the vote counted, Tisza was set to win 138 seats in the 199-member parliament, enough for a two-thirds constitutional majority, according to data from the National Election Office (NVI).
“Hungary, Poland, Europe. Back together! Glorious victory, dear friends!” Tusk wrote on X.
“Ruszkik haza! (Russians, go home)," he added in Hungarian.
Tisza leader Peter Magyar said his first foreign trip would be to Warsaw, followed by visits to Vienna and Brussels.
Hungarian Prime Minister Viktor Orban conceded defeat after the centre-right Tisza party secured a sweeping parliamentary victory, dealing a blow to his right-wing allies in Europe and across the Atlantic.
Orban’s ruling Fidesz party was expected to secure 54 seats.
Sunday's vote was closely watched in Warsaw, with Magyar pledging to strengthen ties with Poland if he takes power.
Tusk said ahead of the vote that the Hungarian election could mark a turning point for Europe following a recent wave of gains by pro-Russian and Eurosceptic groups.
Magyar had cast the election as decisive for Hungary’s future, framing it as a choice between "East or West, a failing state or a functioning one, corruption or a fair public sphere."
He said a new government would prioritise anti-corruption measures, strengthen Hungary’s position in the EU and NATO, unlock frozen EU funds and improve relations with Poland.
Analysts say the end of Orban's rule could have significant implications for Ukraine, potentially easing Hungary’s opposition within the EU and opening the way for new financial support for Kyiv.
'Hungary has chosen Europe': EU's von der Leyen
European Commission President Ursula von der Leyen said after partial results that "Hungary has chosen Europe."
Orban's defeat could also deprive Russian President Vladimir Putin of a key ally within the EU, the Reuters news agency reported.
Despite support from US President Donald Trump and other right-wing figures, Orban’s campaign was weakened by voter dissatisfaction over economic stagnation, rising living costs and allegations that business figures close to the government had accumulated significant wealth.
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Source: PAP, IAR, Reuters