The get-together is set to discuss trade and global challenges as the prime ministers of the V4 countries, Poland, Hungary, the Czech Republic and Slovakia, first convene among themselves, according to officials.
The South Korean president will then join them for a plenary session, followed by a working lunch, Polish state news agency PAP reported.
During the day, Morawiecki is also due to talk privately with Moon Jae-in and then with Hungarian Prime Minister Viktor Orban, public broadcaster Polish Radio's IAR news agency reported.
Piotr Müller, the spokesman for the Polish government, told reporters that the Budapest meeting would provide an opportunity to debate "mutual relations, particularly trade and investment, energy and infrastructure, cooperation in science and culture, as well as the role of the International Visegrad Fund."
The leaders are also set to discuss key global challenges, such as the situation in Afghanistan, migrations, the climate and how countries can work together towards post-pandemic recovery, Müller added, as quoted by PAP.
South Korea is Poland's second-biggest trade partner in Asia, the news agency reported.
Müller told reporters that South Korean firms were "increasingly involved" in infrastructure and manufacturing projects in Poland.
Thursday's "V4+South Korea" meeting is hosted by Hungary, which holds the year-long rotating presidency of the regional Visegrad Group until mid-2022.
The previous such get-together took place in late 2015 in Prague, PAP reported.
Source: IAR, PAP