The experienced duo top the charts for wickets taken, with 39-year-old Anderson taking 640 in 169 matches, while Broad follows closely behind with 537 in 152 appearances.
Yet, under new management and directorship following England's dismal Ashes defeat, neither will take part in next month's West Indies tour.
Chris Silverwood recently left his role as England head coach after receiving criticism for his management of the side during The Ashes series.
Silverwood came under fire because of his controversial team selections and rotations, which saw both Broad and Anderson miss out on the opening match of the series.
It was a decision that contributed to his sacking, but even with Sir Andrew Strauss replacing Ashley Giles as managing director and Paul Collingwood taking temporary charge as head coach, a similar decision has been made.
What's more, Broad and Anderson were responsible for most of England's - admittedly rare - good moments Down Under, yet they've been snubbed once more.
The decision was made on Tuesday evening, after a selection meeting took place involving interim head coach Paul Collingwood, acting director of cricket Sir Andrew Strauss and head scout James Taylor.
Neither Broad or Anderson have given any indication that they plan to retire anytime soon, with reports suggesting that they're both waiting for confirmation of a new head coach before revealing their long-term plans.
Full England Test squad:
Joe Root (Yorkshire) (C)
Jonathan Bairstow (Yorkshire)
Zak Crawley (Kent)
Matthew Fisher (Yorkshire)
Ben Foakes (Surrey)
Dan Lawrence (Essex)
Jack Leach (Somerset)
Alex Lees (Durham)
Saqib Mahmood (Lancashire)
Craig Overton (Somerset)
Matthew Parkinson (Lancashire)
Ollie Pope (Surrey)
Ollie Robinson (Sussex)
Ben Stokes (Durham)
Chris Woakes (Warwickshire)
Mark Wood (Durham)
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