Left-handed opener Cook, England's all-time leading run-scorer, retired from international duty after bringing down the curtain on his illustrious 12-year Test career with a farewell century against India at the Oval earlier this month.
That left England with an opening batsman vacancy.
They have now turned to Burns, who captained Surrey to the County Championship title this season.
Burns has been the leading run-scorer in the English top flight this season, scoring 1,319 Championship runs at an average of over 69.
Fellow opener Keaton Jennings was retained despite struggling against India, with the uncapped Joe Denly, another top-order batsman, also included.
Warwickshire paceman Olly Stone was the third uncapped player in the squad.
The 32-year-old Denly returns to the England set-up for the first time since 2010, when he earned nine one-day international caps and played five Twenty20s.
His leg-spin bowling could also prove useful in Sri Lanka, where pitches often provide plenty of turn.
The 24-year-old Stone, who was named in England's squad for the first time earlier this week for the preceding white-ball series, has taken 37 wickets at just 12 piece for Warwickshire in the County Championship this season.
Somerset left-arm spinner Jack Leach returns to the England squad for the first time since he made his debut in New Zealand in March and is one of three specialist spinners named alongside Worcestershire's Moeen Ali and Yorkshire leg-spinner Adil Rashid.
But there was no place for Hampshire batsman James Vince, who was on the fringes of the Test squad during the recent home international season.
- 'Consistent' Burns -
"Rory Burns, who has led Surrey to the Championship title, has been the most consistent run-scorer in county cricket in recent seasons and fully deserves his elevation to the Test squad," said England national selector Ed Smith, who took over at the start of the current English season.
"Joe Denly has had an excellent season with bat and ball and has matured into one of the leading players in county cricket," added former England batsman Smith, who played alongside Denly at Kent.
"Olly Stone is an exciting talent who bowls with pace and skill."
Stuart Broad was included despite speculation he might be rested and the experienced paceman is set to continue his new-ball partnership with James Anderson, now the most successful fast bowler in Test history after breaking Australia great Glenn McGrath's record of 563 wickets at the Oval, where England completed a 4-1 series win over top-ranked India.
Meanwhile Jonny Bairstow was listed as England's wicket-keeper.
Injury meant he spent part of the India series playing as a specialist batsman, with one-day gloveman Jos Buttler taking over behind the stumps.
Buttler is also in the squad but listed as a batsman.
England have two warm-up games in October and November before facing Sri Lanka in the first of three Tests in Galle starting on November 6.
Squad: Joe Root (Yorkshire, capt), Moeen Ali (Worcestershire), James Anderson (Lancashire), Jonny Bairstow (Yorkshire, wkt), Stuart Broad (Nottinghamshire), Rory Burns (Surrey), Jos Buttler (Lancashire), Sam Curran (Surrey), Joe Denly (Kent), Keaton Jennings (Lancashire), Jack Leach (Somerset), Ollie Pope (Surrey), Adil Rashid (Yorkshire), Ben Stokes (Durham), Olly Stone (Warwickshire), Chris Woakes (Warwickshire)
First Published: September 21, 2018, 9:37 PM IST