Hobby Lobby’s president Steve Green said he is in the process of repatriating 11,500 antiquities to the Iraqi and Egyptian governments, bowing to what he called justified criticism from scholars and authorities over the ways he amassed a vast collection for the Museum of the Bible in Washington, D.C.

Mr. Green, who is also chairman of the museum’s board, said the Bible museum is helping his family collection coordinate the return of around 5,000 ancient papyrus fragments and 6,500 ancient clay objects because the artifacts lack reliable provenance, or ownership histories. Artifacts without a paper trail are worrisome because they could have been previously looted or stolen.

“One area where I fell short was not appreciating the importance of the provenance of the items I purchased,” Mr. Green said. When he started collecting biblical-era antiquities in 2009, “I knew little about the world of collecting.”

“The criticism of the museum resulting from my mistakes was justified,” he added.

The planned repatriation will likely serve as a coda to one of the art world’s biggest antiquities scandals in recent years, sparking international investigations and casting a shadow over the Oklahoman’s efforts to transform his own Bible-collecting hobby into a world-class museum.