Christie said in a statement that the law will help keep weapons away from criminals. Previously, he was less effusive, saying it was redundant because it mostly codified existing practice but was nonetheless "worthwhile."
His approval comes after the Legislature reworked parts of the bill following Christie's previous conditional veto of it.
The governor said that provisions calling for public reports to be produced about some of the information would have violated a federal law banning making such information public.
Last month, Christie vetoed two bigger pieces of gun legislation. One would have banned .50-caliber rifles and the other would have overhauled the state's gun permit law.
With Friday's bill signing, Christie pointed out that the Brady Campaign to Prevent Gun Violence had already ranked New Jersey's gun laws, which include an assault weapons ban and a seven-day waiting period to buy guns, as the second-toughest in the nation.
The state's lawmakers have passed several new gun-control measures since last year's massacre of 20 schoolchildren in Newtown, Conn.