Matt Damon will star in “Hereafter,” Clint Eastwood’s next producing-directing project for Warner Bros., with lensing on the thriller set to begin this fall.

For Eastwood, the project’s a move into supernatural territory. Warner Bros. is keeping the logline under wraps beyond describing the project as a thriller in the vein of “The Sixth Sense.”

Peter Morgan, who received an Oscar nomination for “Frost/Nixon,” penned the script.

Eastwood’s producing through his Warner-based Malpaso banner with Kathleen Kennedy and Eastwood producing partner Robert Lorenz. Kennedy and Marshall’s company will receive a production credit.

Steven Spielberg, Frank Marshall, Morgan and Tim Moore are exec producing. Project was originally set up at DreamWorks.

Damon can currently be seen in Steven Soderbergh’s “The Informant.” He will be seen starring opposite Morgan Freeman in Eastwood’s “Invictus,” the true story of how Nelson Mandela joined forces with the captain of South Africa’s underdog rugby team to help unite their country. “Invictus” is set to open Dec. 11.

Eastwood first expressed interest in “Hereafter” late last year when it was still at DreamWorks, which had picked up Morgan’s spec in March 2008 when it was still a part of Paramount. DreamWorks held onto the project as part of its separation pact with the Melrose studio (Daily Variety, Nov. 14).

Eastwood previously worked with Spielberg on “Flags of Our Fathers” and “Letters From Iwo Jima,” both of which Spielberg produced.