The match, which begins on May 22nd at Trent Bridge, is Zimbabwe's first test in England in 22 years and marks the start of the English summer.
Cook has picked up 318 first-class wickets and the 27-year-old made a name for himself on the England Lions tour of Australia where he took 13 wickets in three matches. Cox is a 24-year-old wicketkeeper.
Meanwhile, fast bowler Josh Tongue has recovered from injuries and earned a recall to the test squad for the first time since the 2023 Ashes.
England squad for Zimbabwe test
Ben Stokes (Durham), Gus Atkinson (Surrey), Shoaib Bashir (Somerset), Harry Brook (Yorkshire), Sam Cook (Essex), Jordan Cox (Essex), Zak Crawley (Kent), Ben Duckett (Nottinghamshire), Ollie Pope (Surrey), Matthew Potts (Durham), Joe Root (Yorkshire), Jamie Smith (Surrey), Josh Tongue (Nottinghamshire).