The two Toms rose to prominence when their video 'High Renaissance Man' went viral, and have since been nominated for Best Newcomer at the Edinburgh Comedy Awards. They made their television debut on Channel 4's Comedy Lab.
Directed by Simon Dormandy, Waiting for Godot runs at the Arcola Theatre, Studio One from 7 May to 14 June 2014.
The play centres on two friends, one of whom went on the anti-war protest, the other of whom stayed at home and watched TV.
Bartlett's previous plays include Love Love Love (UK tour and Royal Court), and adaptations of Medea (which starred Stirling in the title role) and Chariots of Fire.
A co-production with Paines Plough, An Intervention runs at the Watford Palace Theatre from 19 April to 3 May 2014.
Tonight at 8.30 comprises a collection of nine one-act plays, encompassing the "full kaleidoscopic range of Coward's writing."
Throughout the run at the Nuffield and the tour there will be opportunities for audiences to see all nine plays in special 'triple bill days'.