The magazine says Wright and Penn, who have had a tumultuous relationship, have agreed to share custody of their 16-year-old son, Hopper Jack. Court papers cite "irreconcilable differences" for the split.
A representative for Wright did not return an e-mail seeking comment.
The couple married in April 1996. The Penns have twice before filed for divorce or separation only to dismiss their petition a short time later.
Sean Penn won an Oscar for his role in "Milk" at the Academy Awards in February but did not thank his wife in his acceptance speech.