Hampshire batsman Vince could well make his Test debut in Leeds, given there is now a vacancy following the retirement through illness of James Taylor.
Nottinghamshire paceman Ball, meanwhile, looks set to compete with Steven Finn for the third seamer role in an attack set to be led by James Anderson and Stuart Broad.
Vince, 25, already has five England limited-overs caps. His batting style has been compared to that of former England captain Michael Vaughan.
The Hampshire captain has made a sound start to the season, including scoring a hundred against county champions Yorkshire at Headingley in Leeds, northern England.
Ball, also 25, has made his case with 19 Championship wickets for Nottinghamshire so far this season.
“Both Jake Ball and James Vince thoroughly deserve their opportunity, having performed well with the England Lions (the national A or reserve side) and starting the season in good form with their respective counties,” said national selector James Whitaker in an England and Wales Cricket Board statement.
“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.”
England will again be captained by Alastair Cook, with the Essex left-hander needing just 36 more runs to become the first Englishman to score 10,000 in Tests.
Alex Hales looks set to keep his place as Cook’s opening partner, with Nick Compton in line to be given another opportunity at number three in what will be England’s first Test campaign since their series win in South Africa.
At Headingley two years ago, Sri Lanka won a thrilling match with just one ball remaining to claim a 1-0 Test series victory.
This time around Sri Lanka are without batting greats Kumar Sangakkara and Mahela Jayawardene, both now retired from international cricket.
“Sri Lanka are a young side, and we expect a strong series between the two teams to start the summer of international cricket,” said Whitaker.
The first Test, which starts at Headingley on May 19, is the first of a three-match series.
England have also named a 30-man performance squad for their home season, including 22 players who have either central or incremental contracts based on international appearances over the last year.
England Test squad:
Alastair Cook (Essex, capt), Moeen Ali (Worcestershire), James Anderson (Lancashire), Jonny Bairstow (Yorkshire, wkt), Jake Ball (Nottinghamshire), Stuart Broad (Nottinghamshire), Nick Compton (Middlesex), Steven Finn (Middlesex), Alex Hales (Nottinghamshire), Joe Root (Yorkshire), Ben Stokes (Durham), James Vince (Hampshire).