Superior Court Judge Henry Hight signed an order earlier this week siding with the state and declaring the document belongs to North Carolina.
Cooper said in a statement that the decision ends all remaining claims to the copy.
"The Bill of Rights is more than words on a piece of paper," Cooper said.
"It's a powerful part of our history and a symbol of our liberty. It belongs to the people and it belongs here in North Carolina, for good."
North Carolina officials have held the faded parchment since 2005, two years after it was recovered by federal authorities in a sting operation.
The copy of the document listing the rights enjoyed by United States citizens was made in 1789. During the Civil War, it was taken by a Union soldier who sold it in 1866 to a buyer in Ohio.
That person's family sold it to Connecticut antiques dealer Wayne Pratt and businessman Robert Matthews in 2000 for $200,000. In March 2003, an FBI agent posing as a museum buyer at a meeting in Philadelphia pretended to purchase the paper from Pratt and Matthews for $5 million.
Pratt relinquished his claim to the document in September 2003, but Matthews did not. In 2006, Matthews' attorney said his client believed the state had seized the document illegally.
The News & Observer of Raleigh reported that the state did not pay Matthews any money, but did agree to let him claim a tax deduction for a charitable contribution to the state. The state also agreed to let an appraiser for Matthews examine the document to establish its donation value.
Matthews has said previously that the document has a value of $30 million on the private market.
The document lists 12 proposed amendments to the U.S. constitution presented to the states in 1789. The amendments were ultimately reduced to 10.