The FCC imposed conditions on the deal related to data roaming and interference.
The commission voted 3-1, with Commissioner Michael Copps dissenting.
"I could be persuaded, with the right set of pro-consumer conditions, to concur in the transaction," Copps said in a statement. "While much of the competitive analysis in today’s order is strong, the conditions the Commission does attach strike me as falling short of advancing the public interest demand."
He expressed concern about concentrating more control of the airwaves in the hands of one of the two leading wireless companies, with the other being Verizon.
Copps, who has served on the FCC for 10 years, will retire at the end of the month.