Robson, who only moved to England six years ago after playing for Australia under-19s, joins Chris Jordan and Moeen Ali in a 12-man squad.
The Middlesex batsman, 24, is averaging 51 this season while opening with Australia opener Chris Rogers.
He qualified to play for England via his English mother and was officially eligible to play for England in August last year.
Robson carved up on tour to Australia and India with the England performance programme team and was with the England squad when they were spanked 5-0 in the Ashes Down Under.
Sussex quick bowler Jordan, who grew up in Barbados, has impressed in the ODI series against Sri Lanka with 12 wickets.
Ali, who was actually born in England, is a classy left-handed batsman whose spin will play a key role in the Tests for Alastair Cook.
Wicketkeeper Matt Prior has also been included despite playing just one county game this year as a keeper.
England squad: Alastair Cook (Essex), Moeen Ali (Worcestershire), James Anderson (Lancashire), Gary Ballance (Yorkshire), Ian Bell (Warwickshire), Stuart Broad (Nottinghamshire), Chris Jordan (Sussex), Liam Plunkett (Yorkshire), Matt Prior (Sussex), Sam Robson (Middlesex), Joe Root (Yorkshire), Chris Woakes (Warwickshire).
Sri Lanka squad: Angelo Mathews (capt), Lahiru Thirimanne (vice-capt), Dimuth Karunaratne, Kaushal Silva, Kumar Sangakkara, Mahela Jayawardene, Prasanna Jayawardene (wk), Dinesh Chandimal, Rangana Herath, Dilruwan Perera, Shaminda Eranga, Nuwan Kulasekara, Nuwan Pradeep, Chanaka Welagedara, Dhammika Prasad.
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