The James Bond actor will star as Iago in the play staged by the New York Theater Workshop (NYTW), with Selma actor Oyelowo in the title role.
The play will be presented in a 199-seat theatre for a limited run, although dates are yet to be announced.
It will be directed by Sam Gold, who won a Tony this year for Fun Home.
The director told the New York Times he and Craig had been in talks for some time to collaborate on a theatre project, before reaching out to Oyelowo.
'Sublime actors'
He added he was excited to present the play in a small theatre because of the intimacy it would afford, but said it was too early to describe the production in any detail.
"When Sam Gold came to us with the beginning sketches of this production, with these two sublime actors, it seemed the perfect next step for us to take together," NYTW artistic director James Nicola told Deadline.
"I'm eager to see what these original, creative artists come up with in response to Shakespeare's enduring tragedy."
Although the NYTW has hosted a number of productions which went on to Broadway success, including Once and Peter and the Starcatcher, Nicola said a Broadway transfer of Othello was unlikely given the limited availability of the actors.
Craig - who will be seen on the big screen in 007 film Spectre later this month - recently appeared on Broadway in 2013 in a revival of Harold Pinter's Betrayal opposite his wife, Rachel Weisz, and Rafe Spall.
In 2009, he also appeared opposite Hugh Jackman in a Broadway production of A Steady Rain.
Oyelowo has a long list of theatre credits to his name, beginning his stage career in 1999 with the Royal Shakespeare Company.  He was the first black actor to play an English king in a major Shakespeare production in the RSC's 2001 staging of Henry VI.
Among his other credits include Prometheus Bound, The White Devil and The Suppliants.
British stars David Oyelowo and Daniel Craig are to star together in an Off Broadway production of Shakespeare's Othello next autumn.