The Herd, which runs from 13 September to 12 October, is Kinnear's first play and will be directed by Howard Davies, who recently directed Kinnear in The Last of the Haussmans and Burnt by the Sun at the National.
It's billed as "a witty and heartfelt look at a family falling apart and pulling together when life doesn't turn out quite the way they imagined," and is set around a 21st birthday celebration.
Kinnear's myriad acting credits include Hamlet, The Revenger's Tragedy and The Man of Mode (for which he won an Olivier Award) at the National, where he can soon be seen starring opposite Adrian Lester in Othello.
The Herd is preceded by Cush Jumbo's debut play Josephine and I, which centres on legendary American entertainer Josephine Baker and her impact on a "modern day girl".
Starring Jumbo, whose recent acting work includes Julius Caesar (Donmar Warehouse) and She Stoops to Conquer (National Theatre), it runs from 12 July to 10 August.
The new season at the Bush - which relocated to the former Shepherd's Bush Library in 2011 - will also see the UK premiere of Ayad Akhtar's award-winning play Disgraced (17 May-5 June), directed by Nadia Fall, and the European premiere of Australian playwright Declan Greene's Moth (29 May-8 June), directed in the Attic space by Prasanna Puwanarajah in assocation with HighTide.
November will see the return of RADAR, the Bush's new writing festival, following last year's inaugural event.
Artistic director Madani Younis said today he was "thrilled" to be granting "three major talents" their playwrighting debuts in the coming months. Currently at the Bush, MONEY the game show opens tonight (6 February 2013, previews from 31 January) and continues to 2 March.