Gill's play Versailles, a reflection on the legacy of World War One, opens the season from 27 February to 5 April 2014 (previews from 20 February).
The play, one of a number marking the 100th anniversary of the outbreak of the 1914-18 conflict next year, centres on a young English man who is sent to partake in the controversial peace treaty that was signed in 1919.
The second play of the season is Privacy, by This House author James Graham, which runs from 22 April to 31 May 2014 (previews from 10 April).
The play, which has been developed by Graham in collaboration with Donmar artistic director Josie Rourke, was prompted by the recent revelations of Edward Snowden and examines the impact of social media and 'big data'.
According to press material, "Privacy draws on Graham's interviews with journalists, politicians and analysts and poses the question: Is there any such thing as privacy in the 21st century?"
Friel adapts Turgenev
The final play in the season is Fathers and Sons by Brian Friel, after the novel by Ivan Turgenev. Directed by Lyndsey Turner, marking her return to the Donmar, the production runs from 10 June to 26 July 2014 (previews from 5 June).
Turgenev's novel centres on two young men who arrive at a country estate, fresh from university: one, the son of the landowner, the other a brilliant and charismatic radical, proclaiming a dangerous new philosophy. But their warm welcome cools as the new house guest attacks the values of his hosts, bringing to the surface the tensions between one generation and the next.
Brian Friel has written over 30 plays across six decades. He is best known for Translations, Philadelphia, Here I Come! and Dancing with Lughnasa, which won Best Play at the Tony Awards, Olivier Awards and New York Drama Critics Circle.
Lyndsey Turner directed Philadelphia, Here I Come! at the Donmar in 2012. Her other recent credits include Chimerica, which recently transferred from the Almeida to the West End, and Posh (Royal Court and West End).
Next year the Donmar will also, as previously announced, transfer its reival of Conor McPherson's The Weir to the West End. And its recent premiere production of McPherson's The Night Alive will transfer to the Off-Broadway Atlantic Theater in December.
In January 2014 work will be completed on Donmar Dryden Street, a new space that will bring all of the theatre's off-stage work under one roof for the first time. It will offer state of the art rehearsal facilities, a music room and the Clore Studio, an educational space.