A revamped version of George Gershwin’s “Porgy and Bess,” starring Audra McDonald, Norm Lewis and David Alan Grier, will go to Broadway soon after it completes its run, previously announced, at the American Repertory Theater in Cambridge, Mass.

Producers announced on Wednesday that the show — which plays down its roots as an opera and features a reworked book by the Pulitzer Prize-winning playwright Suzan-Lori Parks and new arrangements by Diedre Murray — will open at the Richard Rodgers Theater on Jan. 12, with previews beginning on Dec. 17.

Diane Paulus, the artistic director at the A.R.T., will direct “Porgy and Bess.” Kicking off the company’s season, the show is slated to run from Aug. 17 to Oct. 2, with an opening night on Aug. 31.

When the A.R.T. engagement was first announced, Ms. Paulus said that she and the creative team intended the show to “have a future life” beyond Cambridge. She said then that the Gershwin estate wanted to turn the classic work into a musical and “bring it to the audiences of today.”

The casting of Ms. McDonald as Bess, Mr. Lewis (“Sondheim on Sondheim”) as Porgy, Mr. Grier (“Race”) as Sportin’ Life, and Joshua Henry (“The Scottsboro Boys”) as Jake made clear this was unlikely to be just a short regional run. And the producers, Jeffrey Richards and Jerry Frankel, expressed optimism about Broadway after workshops and a developmental performance for investors in May.

“Porgy and Bess” had its premiere in Boston in 1935 and ran briefly on Broadway soon after. The show had months-long revivals there in 1942 and 1953, but in recent decades it has remained in opera houses.