Despite Bayern Munich's efforts to prise him away from North London, where he is only under contract for another year, Kane made the trip to Perth and wears the captain's armband in the absence of Hugo Lloris.
With Lloris being left at home to explore a move away, Guglielmo Vicario comes in for his first start in goal, while James Maddison and Manor Solomon will also make their non-competitive debuts.
Japhet Tanganga and Sergio Reguilon - two players who fell out of favour under Antonio Conte - are also offered starts in defence, as Postecoglou implements his tried-and-tested 4-3-3 system.
Tanguy Ndombele misses out after taking a knock in training on Monday, while Eric Dier, Djed Spence and Son Heung-min have also failed to make the cut for Postecoglou's first game in charge.
Meanwhile, West Ham boss David Moyes makes three changes to the side that defeated Perth Glory 6-2 at the weekend, bringing in Angelo Ogbonna, Jarrod Bowen and Divin Mubama for Luizao, Daniel Chesters and Gianluca Scamacca.
Tottenham Hotspur: Vicario; Porro, Romero, Tanganga, Reguilon; Skipp, Bissouma, Maddison; Kulusevski, Kane, Solomon
Subs: Austin, Whiteman, Royal, Sanchez, Udogie, Davies, Sarr, White, Devine, Hojbjerg, Perisic, Lo Celso, Richarlison
West Ham United: Fabianski; Laing, Zouma, Ogbonna, Emerson; Bowen, Potts, Downes, Fornals; Mubama, Ings
Subs: Anang, Knightbridge, Luizao, Cresswell, Swyer, Chesters, Coventry, Scamacca