T-Mobile US Inc. won approval from U.S. national-security officials for its planned takeover of Sprint Corp., bringing the two rivals a step closer to closing their roughly $26 billion combination.

The Committee on Foreign Investment in the U.S., or Cfius, told the companies Monday that it had cleared the union of the No. 3 and No. 4 carriers by subscribers after several months of negotiations with company representatives, the companies said.

The...