The paper said a studio official has confirmed that Singer signed Friday to take over the project, which has had several false starts -- going back to the '90s when Nicolas Cage was supposed to have played the Man of Steel for director Tim Burton.
Singer told Variety he has been interested in Superman for years.
"In fact, it was the Richard Donner classic film that was my day-to-day inspiration in shaping the 'X-Men' universe for the screen," he said. "I feel that Superman has been late in his return and it is time for him to fly again."
Singer is expected to work with "X-2" writers Michael Dougherty and Dan Harris to draft a screenplay. No one has been chosen yet to play the title role.
As a result of taking the "Superman" gig, Variety said it appeared as though Singer would not be directing the third "X-Men" movie.
"Charlie's Angels" director McG pulled out of the "Superman" project earlier this month.