It will be the first official visit at the level of presidents since the two countries gained independence.
During his visit, the Croatian president is due to meet Prime Minister Gediminas Kirkilas, Parliament Speaker Viktoras Muntianas, Foreign Minister Petras Vaitiekunas and Defence Minister Juozas Olekas.
The governments of the two countries are expected to sign an agreement on cooperation in culture and tourism.
On the second day of the visit, Mesic is scheduled to meet Croatian language teachers and students at Vilnius University and deliver a talk at the Institute for Foreign Affairs and Political Sciences.