O'Bannon, a Democrat, said a new monument will be erected on the grounds of the Statehouse this summer that will feature the commandments, the Bill of Rights and the preamble to the U.S. Constitution.
The Indiana Civil Liberties Union argues the law, which takes effect July 1, violates the constitutional separation of church and state. It is likely to sue shortly after the monument is in place, the Associated Press reported.
"Obviously we will have an obligation to get involved in litigation, and if the court rules we are right and the Legislature was wrong, it's going to cost the taxpayer an awful lot of money," said John Krull, executive director of the group.
He recommends that schools and governments hold off on displaying the commandments in their buildings.
But O'Bannon said in a statement that he believes the law is constitutional.
"For more than three decades, a monument inscribed with the Ten Commandments stood on the Statehouse lawn as a reminder of some of our nation's core values," he said. "Soon those words will stand alongside the abiding principles of our form of government, especially its protections of individual rights."
The old monument, erected in 1958, was removed in 1991 after it was the subject of vandalism.