The Comptroller, with the advice of the Attorney General, may adjust and settle upon equitable principles, without regard to strict legal rules, any doubtful or disputed account or claim in favor of the Commonwealth which may have been standing on the books of his office not less than two years, and may, with the like advice, dismiss any proceedings instituted by him; but before such adjustment or settlement can in any wise affect the rights of the Commonwealth it shall be approved and endorsed by the Attorney General and shall then be submitted to the supervision of the judge of the Circuit Court of the City of Richmond, accompanied by a written statement signed by the Comptroller of the facts and reasons which, in his opinion, render such adjustment or settlement just and proper. When such judge endorses the same with his written approval, signed in his official character, it shall be considered and treated as valid and binding.