The Fringe programme for the venue, which will re-open on George Street in July following a £9.3 million refurbishment project, also includes the wrestler Mick Foley, the Labour politician Tony Benn, Les Dennis, the popular stand up Stewart Lee and Jerry Sadowitz.
The Stand Comedy Club is the new organiser of the venue, led by director Tommy Sheppard. He said: "In bidding to run the Assembly Rooms during the Edinburgh Festival Fringe, we promised to deliver a world-class programme, provide more generous deals for artists and keep prices down for the public.
"I'm delighted to say we've done just that ... people who know the building of old will be delighted by this programme and we hope to attract many others for the first time."
Ms Lochhead will present a daily show of poems, monologues, lyrics, theatre pieces and special guests.
Two National Theatre of Scotland productions will also be staged in the Assembly Rooms – Appointment with the Wicker Man and a one-woman show, Love Letters to the Public Transport System.
David Hayman will star in Six and a Tanner and there will be a music bill including Karen Matheson, James Grant and Jimmie MacGregor.
A new play by Dave Florez, The Intervention, will star Arabella Weir, Mike McShane and Phil Nichol.
Tony Benn will attend two events previewing a new documentary film about his life in politics.
The Assembly Rooms Fringe will be operated for the next five years by Edinburgh-based Salt 'n' Sauce Promotions Ltd, best known for running the Stand Comedy Clubs in Edinburgh, Glasgow and Newcastle.