Uncapped James Vince and Jake Ball are also included with Hampshire batsman Vince appearing set for his debut.
The line-up includes Nick Compton - who has kept his spot as England’s likely No 3 - while Ball will have to vie for the third seamer’s role.
Ball, 25, has stated his case with 19 wickets already for Nottinghamshire this summer in the County Championship - having spent the winter with England Lions in the UAE and at a fast-bowling camp in South Africa.
Lions captain Vince, also 25, has five limited-overs caps and was part of the England squad which reached the final of the ICC World Twenty20 in India last month.
He, too, has begun the domestic summer well, including hitting a century against Yorkshire at Headingley.
National selector James Whitaker, said: “Both Jake Ball and James Vince thoroughly deserve their opportunity, having performed well with the England Lions and starting the season in good form with their respective counties.
“James has been a consistent performer for Hampshire and England Lions over the past few years. He is already well-regarded by the England coaches in the short format and now has the opportunity to showcase his skills at Test level.
“Building on his success with the Lions in the winter, Jake has impressed with the ball and has shown excellent control and skill in the opening matches of the county championship.
“If selected, we are confident he will perform very well at international level.”
The first Test starts next Thursday, against opponents who pulled off a last-ditch victory over England at the same venue two years ago to take that series 1-0.
Alex Hales remains as captain Alastair Cook’s opening partner, while Steven Finn is fit again and likely to join the attack in Leeds ahead of Ball.
Whitaker added: “Sri Lanka are a young side, and we expect a strong series between the two teams to start the summer of international cricket.”
England have also named a 30-man performance squad for this summer.
It includes their 22 players who are either centrally-contracted or have incremental contracts based on international appearances over the past year.
Vince’s first Test opportunity comes after the enforced retirement of James Taylor, at the age of just 26, because of his serious heart condition.
The only other player who was in the team which finished the series victory over South Africa in January but is missing from the 12 named on Thursday morning is seamer Chris Woakes.
Ball is preferred after making a persuasive case at the start of this season, particularly when taking two wickets in two deliveries - including Root for a golden duck - in the televised match at home to Yorkshire.
England Test squad (v Sri Lanka at Headingley): AN Cook (capt), MM Ali, JM Anderson, JM Bairstow, JT Ball, SCJ Broad, NRD Compton, ST Finn, AD Hales, JE Root, BA Stokes, JM Vince.