The season, Vicky Featherstone's second since taking over as artistic director in the summer, also sees the Court collaborate with regional theatres across the UK to present London runs of work by Vivienne Franzmann, Jennifer Haley and Gurpreet Kaur Bhatti.
The play centres on an international rock star at the height of his fame, who is reaching the end of the road on his current world tour.
Scott previously worked with Stephens on the one man play Sea Wall, and last appeared at the Royal Court in Mike Bartlett's acclaimed play Cock, in which he starred alongside Ben Whishaw.
Stephens' plays include Port, Wastwater and his multi-award winning adaptation of The Curious Incident of the Dog in the Night-Time.
Birdland is followed in the Downstairs by Tim Crouch's new play Adler & Gibb, which opens on 19 June (previews from 13 June) and continues until 5 July.
According to press material: "Janet Adler and Margaret Gibb were conceptual artists working in New York at the end of the last century... With Adler's death in 2004, however, the compromise began."
Experimental theatre-maker Crouch's credits at the Royal Court include The Author, which toured across the UK and abroad in 2010-11. Adler & Gibb, a co-commission with Center Theatre Group, Los Angeles, is directed by Crouch with Karl James and Andy Smith, and designed by Lizzie Clachan.
And rounding off the Downstairs season is Jennifer Haley's The Nether, directed by new Headlong artistic director Jeremy Herrin.
The play, which won the 2012 Susan Smith Blackburn Prize, is billed as "both an intricate crime drama and a haunting sci-fi thriller that explores the consequences of making dreams a reality."
A co-production with Headlong, it runs from 24 July to 9 August (previews from 17 July).
Upstairs and international
The season opens in the Theatre Upstairs, from 17 January to 1 March 2014 (previews from 13 January), with The Pass by John Donnelly, whose previous plays include The Knowledge at the Bush.
The play centres on two rising football stars and is billed as an "agile new story about sex, fame and how much you're willing to lose in order to win".
The Theatre Upstairs also hosts Vivienne Franzmann's new play Pests, a co-production with Clean Break and the Manchester Royal Exchange.
Running from 2 April to 3 May 2014 (previews from 27 March), it's directed by Lucy Morrison and explores the class divide through the lives of two sisters.
And Khandan (Family) by Gurpreet Kaur Bhatti (11 June-28 June 2014) focuses on a Punjabi British family struggling to deal with a father's legacy and hold the family business together.
Elsewhere next year, New York Theatre Workshop will present Caryl Churchill's Love and Information, directed by James Macdonald, which premiered at the Royal Court in 2012.
Meanwhile the Beckett trilogy Not I, Footfalls and Rockaby starring Lisa Dwan will follow its January run at the Royal Court with a national and international tour later in 2014.
Vicky Featherstone said: "With six fantastic new plays from Gurpreet Kaur Bhatti, Tim Crouch, John Donnelly, Vivienne Franzmann, Jennifer Haley and Simon Stephens - each pushing the boundaries of story-telling and theatre to ask the vital question of what it means to be alive today, the range and subject of these plays will hopefully challenge, thrill and delight audiences.
"As well as three homegrown commissions the Royal Court is beginning its new commitment to significant co-productions with several wonderful partners outside London as well as Clean Break. This means that for the writers and audiences the work will have as wide a reach as possible."
Tickets for the new season go on sale to the general public on 18 November at 10am.