There is also a first Test call-up for fast bowler Olly Stone, two days after his maiden international call when he was named in the ODI squad.
Burns, 28, is the top run-scorer in the County Championship top flight with 1,319, nearly 400 runs more than his nearest competitor, and replaces fellow left-hander Alastair Cook in the 16-strong touring party.
Keaton Jennings’ place at the top of the order was also under threat after he averaged just 18 in 4-1 series win over India but his proficiency against spin bowling looks to have earned him a reprieve.
Burns and Jennings are the only specialist openers in the squad but Denly, who has made three red-ball hundreds this summer, could also be promoted to face the new ball given the expectation that the pitches in Sri Lanka will spin from the first ball.
That Denly is also a useful leg-spin bowler may also have been a factor in his selection ahead of James Vince and Jason Roy.
Meanwhile, Stone’s selection comes on the back of an impressive season with Warwickshire, in which he has taken 37 Championship wickets at a little over 12.
England will hope to make the most of Stone’s pace, he regularly clocks in excess of 90mph, and ability to reverse swing the ball in Sri Lanka, where conventional swing and seam movement will be at a premium.
As expected, Somerset’s Jack Leach is included alongside Moeen Ali and Adil Rashid to provide a third spin bowling option.
The left-armer made his Test debut in New Zealand earlier in the year before losing his place in the team due to a broken thumb sustained 10 days before England’s first Test of the summer against Pakistan.
Stuart Broad is also included despite suggestions he may be rested for the tour while Ollie Pope joins fellow Surrey youngster Sam Curran in the group.
Ben Stokes keeps his place in the squad despite having been charged with bringing the game into disrepute and facing a Cricket Disciplinary Commission hearing in December.
England Test squad: Joe Root (c), Moeen Ali, James Anderson, Jonny Bairstow (wk), Stuart Broad, Rory Burns, Jos Buttler, Sam Curran, Joe Denly, Keaton Jennings, Jack Leach, Ollie Pope, Adil Rashid, Ben Stokes, Olly Stone, Chris Woakes.
England in Sri Lanka 2018 Schedule
1st ODI (D/N) – Dambulla: Wednesday, October 10, 9.30am Sky Sports Cricket and Main Event
2nd ODI – Dambulla: Saturday, October 13, 5am, Sky Sports Cricket and Main Event
3rd ODI (D/N) – Kandy: Wednesday, October, 17 9.30am, Sky Sports Cricket and Main Event
4th ODI – Kandy: Saturday, October 20 5am, Sky Sports Cricket and Main Event
5th ODI (D/N) – Colombo: Tuesday, October 23, 9.30am, Sky Sports Cricket and Main Event
Only T20 – Colombo: Saturday, October 27 2pm, Sky Sports Cricket and Main Event
1st Test – Galle: Tuesday, November 6 to Saturday, November 10, 4am, Sky Sports Cricket and Main Event
2nd Test – Kandy: Wednesday, November 14 to Sunday, November 18, 4am, Sky Sports Cricket and Main Event
3rd Test – Colombo: Friday, November 23 to Tuesday, November 27, 4am, Sky Sports Cricket and Main Event
Comment below to get involved in the debate, but please adhere to our House Rules. If you wish to report any comment, simply click on the down arrow next to the offending comment and click ‘Report’.