Rookie leg-spinner Jeffrey Vandersay was also rewarded for his impressive performance for the Sri Lankan emerging team but there was no place for opener Kaushal Silva and off-spinner Tharindu Kaushal.
Jayasundera struck a century for the Sri Lanka Board President's XI against West Indies in a warm-up match last month and has 10 first class hundreds at a 43-plus average.
"We're just following our policy of picking players on form and giving youngsters who show potential the opportunity," chief selector Kapila Wijegunawardene said of the 24-yer-old's selection.
Vandersay has been in the selection radar since claiming five wickets against the visiting Pakistan team in June and impressive returns for the Sri Lankan emerging team against New Zealand A ensured he joined Rangana Herath and Dilruwan Perera in the three-man spin attack.
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Top order batsman Lahiru Thirimanne could not find a place in the test squad led by Angelo Mathews but remained Mathews' deputy in the ODI team.
Starting on Dec. 10, Sri Lanka will play two tests, in Dunedin and Hamilton, followed by five one-dayers and two Twenty20 Internationals in New Zealand.
Test squad: Angelo Mathews (captain), Kusal Mendis, Udara Jayasundera, Dinesh Chandimal, Kusal Perera, Milinda Siriwardene, Kithuruwan Vithanage, Dimuth Karunaratne, Dhammika Prasad, Nuwan Pradeep, Suranga Lakmal, Dushmantha Chameera, Rangana Herath, Dilruwan Perera, Jeffrey Vandersay
ODI squad: Angelo Mathews (captain), Lahiru Thirimanne, Tillakaratne Dilshan, Kusal Perera, Dinesh Chandimal, Milinda Siriwardene, Danushka Gunathilaka, Sachithra Senanayake, Ajantha Mendis, Dhammika Prasad, Lasith Malinga, Nuwan Pradeep, Suranga Lakmal, Dushmantha Chameera, Chamara Kapugedera, Jeffrey Vandersay
Twenty20 squad: Lasith Malinga (captain), Kusal Perera, Shehan Jayasuriya, Dinesh Chandimal, Angelo Mathews, Milinda Siriwardene, Chamara Kapugedera, Kithuruwan Vithanage, Tillakaratne Dilshan, Nuwan Kulasekara, Dushmantha Chameera, Thisara Perera, Jeffrey Vandersay, Sachithra Senanayake, Isuru Udana.
(Reporting by Amlan Chakraborty in New Delhi; editing by Greg Stutchbury)
