Already England's white-ball skipper, Brook leapfrogs Ollie Pope to be Ben Stokes' deputy which could open the door for Jacob Bethell to bat at number three in the Test team.
Jacks has been picked ahead of Rehan Ahmed, Liam Dawson and Jack Leach as the second specialist spinner in the group alongside Shoaib Bashir.
Mark Wood has been selected despite missing the home summer due injury and is one of six seamers in the squad with Jofra Archer, Gus Atkinson, Brydon Carse, Josh Tongue and Matthew Potts, who was added after Chris Woakes was ruled due to dislocated shoulder.
Most of the 16-man squad will first be on tour to New Zealand and will get game time in three T20Is and three ODIs against the Black Caps.
Zak Crawley is in line to make his T20I debut while Ben Duckett, Jamie Smith and Archer are all rested before returning for the ODIs.
Saqib Mahmood will miss the tour after "minor" knee surgery, while Sonny Baker has kept his spot in both white-ball squads despite expensive debuts.
England have not picked a specialist second wicketkeeper for the Ashes with Pope set to take the role of back-up gloveman if Smith is unavailable.
England said that Stokes "remains on track" to be available for the first Ashes Test after injuring his shoulder while bowling against India.
The Ashes kicks off in Perth on 21 November with England only having one warm-up game against the Lions on 13 November ahead of the first Test.
England T20I squad vs New Zealand: Harry Brook (captain), Rehan Ahmed, Sonny Baker, Tom Banton, Jacob Bethell, Jos Buttler (wicketkeeper), Brydon Carse, Jordan Cox, Zak Crawley, Sam Curran, Liam Dawson, Jamie Overton, Adil Rashid, Phil Salt, Luke Wood.
England ODI squad vs New Zealand: Jofra Archer, Ben Duckett, Joe Root and Jamie Smith replace Jordan Cox, Zak Crawley and Phil Salt from the T20I squad.
Tests vs Australia: Ben Stokes (captain), Jofra Archer, Gus Atkinson, Shoaib Bashir, Jacob Bethell, Harry Brook (vice-captain), Brydon Carse, Zak Crawley, Ben Duckett, Will Jacks, Ollie Pope, Matthew Potts, Joe Root, Jamie Smith (wicketkeeper), Josh Tongue, Mark Wood.
England v New Zealand fixtures
T20Is: October 18, 20 (both Christchurch) and 23 (Auckland).
ODIs: October 26 (Mount Maunganui), 29 (Hamilton) and November 1 (Wellington).
Ashes fixtures:
1st Test: November 21-25 (Perth)
2nd Test: December 4-8 (Brisbane, D/N)
3rd Test: December 17-21 (Adelaide)
4th Test: December 25-29 (Melbourne)
5th Test: January 3-7 (Sydney)
Australia took control of the second Ashes Test after the third day following a lower-order batting fightback and then taking six England wickets before the close of play.
Australia went to stumps on the second day of the pink ball Ashes Test on 378-6, the home side leading England by 44 runs on the first innings with four wickets still remaining.
Will Jacks is set to make his first Test appearance in almost three years after England named their starting XI for the second Ashes encounter against Australia that starts in Brisbane on Thursday.
England captain Ben Stokes has come out and said he will accept criticism for his team's performance in the first Ashes Test but has pushed back at jibes that the tourists are "arrogant".
