won five, drawn one and lost one of their last seven Tests there.
Left-arm spinner Rangana Herath and off-spinner Suraj Randiv called the shots in Sri Lanka's last two Test victories at the venue, when they shared 30 wickets against England and Pakistan this year.
Sri Lanka, fresh from their 3-0 one-day series win over the tourists, have also named a third specialist spinner, 19-year-old Tharindu Kaushal, in the squad along with Herath and Randiv.
New Zealand have already lost much of their bowling strength in the absence of match-winning left-arm spinner Daniel Vettori, who was ruled out of the tour after failing to recover from an Achilles strain.
Off-spinner Jeetan Patel is the most experienced specialist slow bowler in the Kiwi squad with 47 wickets in 15 Tests, while leg-spinner Todd Astle has yet to make his Test debut.
Sri Lanka skipper Mahela Jayawardene said his team were looking forward to the Test series.
"We haven't played Test cricket for some time now and we'll try to be as consistent as possible. We still need to improve but we're working hard," he said.
New Zealand need to raise their batting performance as they seek to avoid their fourth successive Test series defeat this year, having already lost to South Africa at home and then in the West Indies and India.
The turning ball caused them major problems on their tour of India in August-September. They failed to cope with off-spinner Ravichandran Ashwin and left-arm spinner Pragyan Ojha to lose the series 2-0.
But the tourists will be pleased with the performance of their fast bowlers in the recent one-dayers, especially in the fifth and final match when they reduced Sri Lanka to 123-8 before rain marred hopes of a victory.
"We have made some improvements and we need to get better. We need to work on all three facets of the game," New Zealand skipper Ross Taylor said after the match.
"We've got seven or eight guys coming over (for Tests)."
The return of batsmen Martin Guptill and Daniel Flynn, and paceman Doug Bracewell, who were not part of the one-day team, has bolstered New Zealand who will be keen to improve their Test record in Sri Lanka.
New Zealand have won only three of their 13 Tests in Sri Lanka.
Sri Lanka (from): Mahela Jayawardene (capt), Angelo Mathews, Tillakaratne Dilshan, Tharanga Paranavitana, Kumar Sangakkara, Thilan Samaraweera, Prasanna Jayawardene, Tharindu Kaushal, Suraj Randiv, Rangana Herath, Dinesh Chandimal, Nuwan Kulasekara, Chanaka Welegedara, Shaminda Eranga, Dhammika Prasad.
New Zealand (from): Ross Taylor (capt), Todd Astle, Trent Boult, Doug Bracewell, Daniel Flynn, James Franklin, Martin Guptill, Chris Martin, Brendon McCullum, Rob Nicol, Jeetan Patel, Tim Southee, Kruger van Wyk, Neil Wagner, Kane Williamson.