Phyllida Lloyd will direct revivals of Julius Caesar and Henry IV and a new production of The Tempest, which are all set in a women's prison.
Harriet Walter will play Brutus in Julius Caesar, King Henry in Henry IV, and Prospero in The Tempest.
The new in-the-round venue will be open for 13 weeks from 23 September.
Julius Caesar and Henry IV were both staged by the company at the Donmar's Covent Garden base in 2012 and 2014 respectively.
The theatre hopes to make 25% of all tickets will be free to 25s and under with a new scheme called Young and Free, funded mainly through sponsorship and philanthropy.
Artistic Director Josie Rourke said: "I remember very clearly the furore created by the idea of an all-female Shakespeare, when Phyllida Lloyd first staged Julius Caesar with Harriet Walter in 2012.
"Phyllida Lloyd's work with this diverse, all-female company has been genuinely ground-breaking and in the intervening four years, theatre has got into the fast lane of debate and change.
"It's time, with these Young and Free tickets, to join together our question about who gets to play these roles with a renewed mission for who gets to experience them."
After its month-long run at the new London venue, The Tempest will transfer to Broadway in October as part of the Donmar's New York season, which runs from July until February 2017.
The James Graham play Privacy, starring Daniel Radcliffe, and Christopher Hampton's Les Liaisons Dangereuses, will also be staged in New York.

The dump, which is thought to cover at least half an acre and is several feet thick, is on private land near Owthorpe Road, Cotgrave.
Fire crews have been called to the site several times, most recently at the weekend.
Nottinghamshire County Council said an Enforcement Notice to clear the site by 1 September had been served.
According to people living nearby, much of the waste had been stored in large plastic bundles but these had been opened when fires started.
Jonathan Smith, from the council, confirmed they had served the notice in April.
He said: "This activity has been done without planning permission and without the prior knowledge of the county council.
"An enforcement notice requiring the removal of all waste from the site and restoration to its former condition has been served on the landowners and other parties who we believe have an interest in the site."
If this is not obeyed the council can clear the land and recover costs and the landowner could face court action.
Tessa Bunby posted on a Cotgrave Facebook page: "I'm sure there is a process to these things but the [local authority] being aware since April is mind-boggling".
Resident Drew Willie said: "You only have to look at it, it is disgusting and it is going to cost a fortune to clean it up.
"There is probably a lot of hazardous waste, the kids are going to come up here and set fire to it again and the fire brigade will have to come and put it out.
"And it is just a waste of resources, all from somebody being irresponsible and dumping stuff here they shouldn't."
London's Donmar Warehouse is to open a temporary theatre in King's Cross to host the company's all-female Shakespeare trilogy.
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A deadline to clear a "disgusting" field of rubbish in Nottinghamshire is close to expiring.