The commission voted 3-2 to approve the deal, it said in a statement.
The companies are still awaiting approval from the Justice Department's Antitrust Division and two other state commissions, for California and Hawaii. It was unclear if state attorneys general will fight the proposed transaction.
The deal has won approval in principle from the Federal Communications Commission and other state public utility commissions.
Critics of the transaction have said it will lead to higher prices for consumers, particularly poorer ones who use prepaid wireless plans that do not require credit checks.
The companies have pledged not to raise prices and said that merging would allow them to more quickly build 5G, the next-generation wireless network.