The 24-year-old Sussex bowler ran through Somerset's tail at Hove last week as he took three wickets in as many balls.
He then repeated the feat against Essex at Chelmsford on Thursday during a return of 5-39, collecting a second hat-trick in eight days.
It has been a breakthrough season for Crocombe, who was briefly added to England's squad for June's second Test against New Zealand, when now-retired former captain Ben Stokes and Gus Atkinson were dropped for disciplinary reasons.
Uncapped Derbyshire batsman Aneurin Donald has been included in England's squad for a preceding T20 series against Sri Lanka.
Donald, 29, scored 489 runs in 12 matches for Derbyshire in the T20 Blast this season.
All-rounder Jacob Bethell continues his recovery from a right knee injury suffered during the white-ball series against India which saw him miss The Hundred, with an England spokesman saying on Friday he "remains on course in his rehabilitation".
England management hope to see Bethell return during the white-ball series in Australia in November.
Ben Duckett is back in the T20 squad after being left out earlier this year, but fellow opener Phil Salt is unavailable due to a right quad problem.
"Aneurin Donald and Henry Crocombe are two promising players who have earned their places on the back of impressive performances in domestic cricket," said England men's national selector Marcus North.
"Aneurin has had an exceptional season for Derbyshire in the Vitality Blast and also with Trent Rockets in The Hundred, while Henry is a player we have had an eye on all summer."
A three-match T20 series starts at Southampton on September 15th, with the first of three ODIs at Chester-le-Street on September 22nd.
England T20 squad
Harry Brook (capt), Jofra Archer, Gus Atkinson, Sonny Baker, Tom Banton, Jos Buttler (wkt), James Coles, Jordan Cox, Liam Dawson, Aneurin Donald, Ben Duckett, Will Jacks, Saqib Mahmood, Jamie Overton, Adil Rashid, Josh Tongue
England ODI squad
Brook (capt), Rehan Ahmed, Archer, Atkinson, Banton, Baker, Buttler (wkt), Cox, Henry Crocombe, Dawson, Duckett, Jacks, Overton, Rashid, Joe Root, Tongue