Leg-spinner Prasanna and fast bowler Eranga got the selectors' nod following their impressive performances in the one-day series, which was won 3-2 by Michael Clarke's Australians.
Prasanna, 26, had a successful one-day debut when he dismissed Shaun Marsh and the Hussey brothers, Michael and David, in one over in the fourth match of the series in Colombo last week.
Eranga, 25, played a strong role in his team's victory in the third one-dayer in Hambantota when he dismissed former skipper Ricky Ponting and Brad Haddin to finish with 2-38 on his debut.
Eranga is one of the four pacemen in the squad alongside Suranga Lakmal, Dhammika Prasad and Chanaka Welegedara.
Sri Lanka also have four frontline spinners to choose from for the first Test which opens at the traditionally spin-friendly Galle International Stadium next Wednesday.
Unorthodox spinner Ajantha Mendis, off-spinner Suraj Randiv and left-arm spinner Rangana Herath are the other slow bowlers in the squad alongside Prasanna.
Sri Lanka Cricket, which had originally named a 15-man squad, later added the seasoned Herath to the line-up.
Sri Lanka's middle-order, led by former captains Kumar Sangakkara and Mahela Jayawardene, will be bolstered by the inclusion of Thilan Samaraweera, who has 4,597 runs in 66 Tests with 12 centuries.
The remaining two Tests will be played in Pallekele (September 8-12) and the Sinhalese sports club in Colombo (Sept 16-20).
Sri Lanka's Test squad: Tillakaratne Dilshan (capt), Tharanga Paranavitana, Kumar Sangakkara, Mahela Jayawardene, Thilan Samaraweera, Prasanna Jayawardene, Angelo Mathews, Suraj Randiv, Rangana Herath, Suranga Lakmal, Chanaka Welegedara, Dhammika Prasad, Shaminda Eranga, Lahiru Thirimanne, Seekkuge Prasanna, Ajantha Mendis.
Copyright AFP (Agence France-Presse), 2011