NEW YORK — A state judge has approved a $1.13 billion settlement between Citigroup Inc. and investors who lost $15 billion by buying mortgage-backed bonds issued by Citigroup prior to the 2008 financial crisis.

Judge Marcy Friedman declared the settlement, negotiated by 18 institutional investors who held 30 percent of the bond investments, to be reasonable. The settlement also provides that Gibbs & Bruns, the law firm that represented the investors, will receive an additional $41 million from Citigroup.