Tawadros will visit various Vatican departments and is set to stay in Rome for several days. His arrival is expected for May 10 or 11, Vatican spokesman Federico Lombardi told AFP.
Tawadros' predecessor Shenouda III met with pope Paul VI in 1973 and the two launched a process of dialogue between their two Christian churches.
"The idea is to celebrate the 40th anniversary of that historic meeting," Lombardi said.
The visit will be part of a European tour during which Tawadros will visit different Coptic parishes -- his first foreign trip since his election in November at a time in which the Coptic minority is faced with rising Islamism in Egypt.
The meeting between Tawadros and Francis will be a further step in greater dialogue between Catholics and Orthodox, after the patriarch of Constantinople, Bartholomew, became the first spiritual leader of the world's Orthodox to attend a papal inauguration of Francis in March.
Another sign of rapprochement is the fact that Tawadros last month attended the inauguration of the new Coptic Catholic patriarch, Ibrahim Sidrak, an unprecedented gesture.