New York Attorney General Letitia James said the state won’t appeal a federal judge’s decision to allow T-Mobile US Inc. and Sprint Corp. to merge, removing another hurdle between the cellphone carriers and their long-planned combination.

“After a thorough analysis, New York has decided not to move forward with an appeal in this case,” Ms. James said in a statement released Sunday. “Instead, we hope to work with all the parties to ensure that consumers get the best pricing and service possible, that networks are built out...