Vince comes into the team in place of the retired James Taylor, while Ball is the joint-leading wicket taker in Division One this season with 19 wickets.
"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," national selector James Whitaker said in a statement.
"Sri Lanka are a young side and we expect a strong series between the two teams to start the summer of international cricket."
England will play three tests against Sri Lanka followed by an ODI series.
England test squad: Alastair Cook (captain), Moeen Ali, James Anderson, Jonny Bairstow, Jake Ball, Stuart Broad, Nick Compton, Steven Finn, Alex Hales, Joe Root, Ben Stokes, James Vince
(Reporting by Simon Jennings in Bengaluru; Editing by Amlan Chakraborty)
