Napolitano, 89, announced last month he would leave office early, citing his age and health, after he reluctantly agreed in 2013 to serve a second term to resolve deadlocked parliamentary elections that year.
Renzi, speaking in the European Parliament in Strasbourg, hailed Napolitano as a long-serving public servant who dedicated his life to Europe and his country.
Napolitano "will stand down within the next few hours with a long list of achievements to his credit," Renzi said as he marked the end of Italy's six-month rotating presidency of the European Union.
The Italian president is elected by parliament and has broad powers which include appointing the prime minister. The head of state can also dissolve parliament and call snap elections.
Once Napolitano steps down, Italy's parliament has to meet within 15 days along with 58 regional deputies to choose a new president.
The winning candidate has to have a two-thirds majority in the first three rounds but only a simple majority is necessary from the fourth round onwards.