The 27-year-old Kalavitigoda came into the reckoning after his impressive 83 against England 'A' this week. Kalavitigoda, whose name did not figure in the preliminary 18-man training pool, has substantial first-class experience having played over 100 first-class matches and averages 32.86 in the domestic circuit.
Left-armer Ruchira Perera has also been included as a replacement for Nuwan Zoysa, who underwent arthroscopic surgery on his knee on Wednesday in Australia.
Champion spinner Muttiah Muralitharan, who will marry this weekend in Chennai, will miss the tour to give his bowling shoulder more time to recover from a second operation in February.
The first Test will be played in Napier from April 4 while the second Test will be played in Wellington from April 11.
SQUAD: Marvan Atapattu (captain), Mahela Jayawardene (vice-captain), Sanath Jayasuriya, Kumar Sangakkara (wicket-keeper), Tillekeratne Dilshan, Thilan Samaraweera, Shantha Kalavitigoda, Upul Chandana, Chaminda Vaas, Rangana Herath, Farveez Maharoof, Nuwan Kulasekara, Lasitha Malinga, Ruchira Perera.